x^2+18x-31=9x+5

Solution for x^2+18x-31=9x+5 equation:

Simplifying
x2 + 18x + -31 = 9x + 5

Reorder the terms:
-31 + 18x + x2 = 9x + 5

Reorder the terms:
-31 + 18x + x2 = 5 + 9x

Solving
-31 + 18x + x2 = 5 + 9x

Solving for variable 'x'.

Reorder the terms:
-31 + -5 + 18x + -9x + x2 = 5 + 9x + -5 + -9x

Combine like terms: -31 + -5 = -36
-36 + 18x + -9x + x2 = 5 + 9x + -5 + -9x

Combine like terms: 18x + -9x = 9x
-36 + 9x + x2 = 5 + 9x + -5 + -9x

Reorder the terms:
-36 + 9x + x2 = 5 + -5 + 9x + -9x

Combine like terms: 5 + -5 = 0
-36 + 9x + x2 = 0 + 9x + -9x
-36 + 9x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-36 + 9x + x2 = 0

Factor a trinomial.
(-12 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

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

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

Divide each side by '-1'.
x = -12

Simplifying
x = -12
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 = {-12, 3}