How do you do algebraic equations and inequalities on this calculator? The keys and the instructions are too small to read.

Look at the face of your calculator, and see if some key has an X marking on it or around it. It may be accessed by pressing an ALPHA key. But before doing that, read the manual to see if your calculator can do algebra. or is a graphing calculator.

There is nothing to solve because you do not have an equation, nor an inequation (inequality). You need an equal sign, >,<, etc.
All you can do with this polynomial is try to factor it. Here is the factored out form
x^3-3x^2-4x=x(x^2-3x-4)=x(x-4)(x+1)
To factor (x^2-3x-4) look for the divisors of -4 whose sum is -3
You cannot do that on your calculator because is does not have a Computer Algebra System or CAS.

The solution set of a linear inequality in two variables (x,y) is one half of the Cartesian plane. The half-plane may or may not contain the boundary line defined by the = sign. Thus it is expected that the calculator shades the relevant half-plane. If you are dealing with nonlinear inequalities the calculator shades inside or outside the curve.
When drawing multiple inequalities the Casio offers you the possibility to shade the regions where ALL conditions (ALL inequalities) are simultaneously satisfied. The other option is OR.
If you are not interested in the shading do not draw inequalities, draw equations (with =).

Choose one of the inequality type graphs

by pressing F3 Type.

Press F6 for the arrow on the right, you will get the other types


For example press F1 to select the Y greater than type graph.

Notice that on the top line Graph Func: Y>. From now on all the graphs you will draw will be Y> some function in X.
Start entering the function. As you start the screen will show Y1>

Enter the function for example sin(X^2). Use the X, theta, T to input the X variable.

Press the EXE key to complete the function line. The screen will look like on the following screen grab
Press the F6 key Draw to get your graph and the shaded region, as on the following picture:

Yes it can be keyed in.
To enter the X, use the ALPHA followed by ). To enter the = sign, you use [ALPHA][CALC].
To use the calculator to SOLVE an equation you must enter the equation, then press [SHIFT][CALC] to (SOLVE). You will be prompted to solve for X. Follow it from there.

As to the case you show, the constant terms will drop and you are left with 26X=0, and the solution is X=0.

Note: The calculator cannot do algebra with letter symbols. It does not have a Computer Algebra System or CAS.

You can do it two ways.
Graphically:
Open the graph utility, enter a function y1= expression(x) where expression(x) is the polynomial. Graph the function y1(x). Play with the window dimensions to display the interesting part of the graph. You can then see if there are any zeros (roots).
While the graph is displayed, press SHIFT F5 (G-Solv). Press F1:Root to look for a root. Read the value of the root at the bottom of the screen (to the left).

Solve utility
Open the QEquation solver, select F2:polynomial, or F3: solver.
The polynomial solve can solve polynomial equations up to degree 6.
The solve solve polynomial and any other type of non algebraic equations

It seems that you are drawing Inequality Graphs.

A. If you are not drawing inequalities, kick the Ineqal application out of memory.

B. If you still want inequality drawing, but just for once want a function graph,

1. you can open the Y= editor. The operation sign (=, less than, less than or equal to,...) will be highlighted in your equation (inequality).
2. Press the [ALPHA] key then press the [Y=] key to select the tab corresponding to the = sign.
   

C. To kick The INEQUAL application from memory,

• Press the [APPS] button.
• In the the new screen display (INEQUAL RUNNING), select [2:Quit Inequal]
• Return to the [Y=] editor screen to make sure that you have function graphs

You can use symbols (X,Y,A,B,C,D, and M, =) to create expressions to use in the SOLV program or to generate a table of values.
To type them you use [ALPHA] followed by the symbol you want. The symbols on the body of the calculator are of the same color as the ALPHA key. The [=] in expressions is different from the general = sign at the bottom of the keypad.

The TI83 does not have a computer algebra system, so you cannot solve algebraic equations for a variable. For that you would need the TI89, TI92 or higher.

You can see images below