x-x^2=12(x+2)

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Solution for x-x^2=12(x+2) equation: 


Simplifying
x + -1x2 = 12(x + 2)

Reorder the terms:
x + -1x2 = 12(2 + x)
x + -1x2 = (2 * 12 + x * 12)
x + -1x2 = (24 + 12x)

Solving
x + -1x2 = 24 + 12x

Solving for variable 'x'.

Reorder the terms:
-24 + x + -12x + -1x2 = 24 + 12x + -24 + -12x

Combine like terms: x + -12x = -11x
-24 + -11x + -1x2 = 24 + 12x + -24 + -12x

Reorder the terms:
-24 + -11x + -1x2 = 24 + -24 + 12x + -12x

Combine like terms: 24 + -24 = 0
-24 + -11x + -1x2 = 0 + 12x + -12x
-24 + -11x + -1x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-24 + -11x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 11x + x2) = 0

Factor a trinomial.
-1((8 + x)(3 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

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

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

Simplifying
x = -8

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-8, -3}

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