-x^2+x+12=2x-8

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Solution for -x^2+x+12=2x-8 equation: 


Simplifying
-1x2 + x + 12 = 2x + -8

Reorder the terms:
12 + x + -1x2 = 2x + -8

Reorder the terms:
12 + x + -1x2 = -8 + 2x

Solving
12 + x + -1x2 = -8 + 2x

Solving for variable 'x'.

Reorder the terms:
12 + 8 + x + -2x + -1x2 = -8 + 2x + 8 + -2x

Combine like terms: 12 + 8 = 20
20 + x + -2x + -1x2 = -8 + 2x + 8 + -2x

Combine like terms: x + -2x = -1x
20 + -1x + -1x2 = -8 + 2x + 8 + -2x

Reorder the terms:
20 + -1x + -1x2 = -8 + 8 + 2x + -2x

Combine like terms: -8 + 8 = 0
20 + -1x + -1x2 = 0 + 2x + -2x
20 + -1x + -1x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
20 + -1x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(5 + x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {4, -5}

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