x^2+5x=x+12

Solution for x^2+5x=x+12 equation:

Simplifying
x2 + 5x = x + 12

Reorder the terms:
5x + x2 = x + 12

Reorder the terms:
5x + x2 = 12 + x

Solving
5x + x2 = 12 + x

Solving for variable 'x'.

Reorder the terms:
-12 + 5x + -1x + x2 = 12 + x + -12 + -1x

Combine like terms: 5x + -1x = 4x
-12 + 4x + x2 = 12 + x + -12 + -1x

Reorder the terms:
-12 + 4x + x2 = 12 + -12 + x + -1x

Combine like terms: 12 + -12 = 0
-12 + 4x + x2 = 0 + x + -1x
-12 + 4x + x2 = x + -1x

Combine like terms: x + -1x = 0
-12 + 4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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 = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

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

Simplifying
x = 2
Solution
x = {-6, 2}