x+3+x+6+2x-2+x^2-2x=31

Solution for x+3+x+6+2x-2+x^2-2x=31 equation:

Simplifying
x + 3 + x + 6 + 2x + -2 + x2 + -2x = 31

Reorder the terms:
3 + 6 + -2 + x + x + 2x + -2x + x2 = 31

Combine like terms: 3 + 6 = 9
9 + -2 + x + x + 2x + -2x + x2 = 31

Combine like terms: 9 + -2 = 7
7 + x + x + 2x + -2x + x2 = 31

Combine like terms: x + x = 2x
7 + 2x + 2x + -2x + x2 = 31

Combine like terms: 2x + 2x = 4x
7 + 4x + -2x + x2 = 31

Combine like terms: 4x + -2x = 2x
7 + 2x + x2 = 31

Solving
7 + 2x + x2 = 31

Solving for variable 'x'.

Reorder the terms:
7 + -31 + 2x + x2 = 31 + -31

Combine like terms: 7 + -31 = -24
-24 + 2x + x2 = 31 + -31

Combine like terms: 31 + -31 = 0
-24 + 2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -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 '(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
Solution
x = {-6, 4}