(x-2)*(x+3)=x*x-8

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Solution for (x-2)*(x+3)=x*x-8 equation: 


Simplifying
(x + -2)(x + 3) = x * x + -8

Reorder the terms:
(-2 + x)(x + 3) = x * x + -8

Reorder the terms:
(-2 + x)(3 + x) = x * x + -8

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = x * x + -8
((3 * -2 + x * -2) + x(3 + x)) = x * x + -8
((-6 + -2x) + x(3 + x)) = x * x + -8
(-6 + -2x + (3 * x + x * x)) = x * x + -8
(-6 + -2x + (3x + x2)) = x * x + -8

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) = x * x + -8

Multiply x * x
-6 + 1x + x2 = x2 + -8

Reorder the terms:
-6 + 1x + x2 = -8 + x2

Add '-1x2' to each side of the equation.
-6 + 1x + x2 + -1x2 = -8 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 1x + 0 = -8 + x2 + -1x2
-6 + 1x = -8 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 1x = -8 + 0
-6 + 1x = -8

Solving
-6 + 1x = -8

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + 1x = -8 + 6

Combine like terms: -6 + 6 = 0
0 + 1x = -8 + 6
1x = -8 + 6

Combine like terms: -8 + 6 = -2
1x = -2

Divide each side by '1'.
x = -2

Simplifying
x = -2

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