Y = x^2 - 6x + 14 - Acer Aspire One AO721-3574 11.6 LED Netbook - Athlon II Neo K125 1.70 GHz - Mesh Black 1366 x 768 WX... (LUSB002197)

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You can't

x=-2

If you're asking how to do this on a particular calculator, please specify the make and mode. If this is homework, be sure to show your work.

For 3x(7x+6x)=0, x=0
For 3x(7x+6x)=1, x=1/39
For 3x(7x+6x)=2, x=2/39
For 3x(7x+6x)=3, x=3/39 or 1/13
For 3x(7x+6x)=4, x=4/39
And so on...

OK, you just have to put those values into the equation, do the math, and see if it works.

-6 * 5/6 - 7 * (-2) = 9 does it?

-5 - (-14) = -5 + 14 = 9 yes it does

You can (and probably should) always check a solution by testing this way. The definition of a solution is a value or set of values that cause the equation to work out. If the test had failed (say we had gotten -6 = 9 before, which is obviously wrong), we'd know that the values weren't a solution.

5x -2(x-2) = 6 -2(-3x-3)
5x -2x +4 = 6 +6x +6 (use the distributive property)
3x + 4 = 6x + 12 (collect terms)
4 = 3x + 12 (subtract 3x from both sides to get all x on one side)
-8 = 3x (subtract 12 from both sides to get only x on one side)
-8/3 = x (divide both sides by 3 to get x by itself)

Check
5(-8/3) -2((-8/3)-2) = 6 - 2(-3(-8/3)-3)
-40/3 -2(-8/3-6/3) = 6 - 2(8-3)
-40/3 -2(-14/3) = 6 -2(5)
-40/3 + 28/3 = 6 - 10
-12/3 = -4 (yes)

The keystrokes you would use to solve the problem is as follows:
(I will use the / to indicate the division symbol)

.5
/
6
X
[( key
12
X
6
)] key
X
1
/
2
X
[( key
6
X
14)] key
=

The first step here is to draw a rough sketch of the two curves, and find the two points they meet. If you set x^3-6x^2+8x = x^3-4x, then you can rearrange this into the quadratic equation 6x^2-12x = 0. Solving this tells you x=0 or 2 : these are the two x values where the curves meet, and they give the bounds on your integral.

When you sketch the curves, you'll see that x^3-4x is below x^3-6x^2+8x, so the thing you need to integrate is (x^3-6x^2+8x)-(x^3-4x), that is, 12x-6x^2. If you integrate this from 0 to 2, you'll have the answer you need!

6x+6=4x+12
Since 4x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 4x from both sides.
6x+6-4x=12
Since 6x and -4x are like terms, add -4x to 6x to get 2x.
2x+6=12
Since 6 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 6 from both sides.
2x=-6+12
Add 12 to -6 to get 6.
2x=6
Divide each term in the equation by 2.
(2x)/(2)=(6)/(2)
Simplify the left-hand side of the equation by canceling the common factors.
x=(6)/(2)
Simplify the right-hand side of the equation by simplifying each term.
x=3

Good Luck