x^2=-x+12

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

Simplifying
x2 = -1x + 12

Reorder the terms:
x2 = 12 + -1x

Solving
x2 = 12 + -1x

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(-4 + -1x)(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-4, 3}