x^2+20x+31=6x-2

Solution for x^2+20x+31=6x-2 equation:

Simplifying
x2 + 20x + 31 = 6x + -2

Reorder the terms:
31 + 20x + x2 = 6x + -2

Reorder the terms:
31 + 20x + x2 = -2 + 6x

Solving
31 + 20x + x2 = -2 + 6x

Solving for variable 'x'.

Reorder the terms:
31 + 2 + 20x + -6x + x2 = -2 + 6x + 2 + -6x

Combine like terms: 31 + 2 = 33
33 + 20x + -6x + x2 = -2 + 6x + 2 + -6x

Combine like terms: 20x + -6x = 14x
33 + 14x + x2 = -2 + 6x + 2 + -6x

Reorder the terms:
33 + 14x + x2 = -2 + 2 + 6x + -6x

Combine like terms: -2 + 2 = 0
33 + 14x + x2 = 0 + 6x + -6x
33 + 14x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
33 + 14x + x2 = 0

Factor a trinomial.
(11 + x)(3 + x) = 0

Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
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 = {-11, -3}