x^2+x-31=32-x

Solution for x^2+x-31=32-x equation:

Simplifying
x2 + x + -31 = 32 + -1x

Reorder the terms:
-31 + x + x2 = 32 + -1x

Solving
-31 + x + x2 = 32 + -1x

Solving for variable 'x'.

Reorder the terms:
-31 + -32 + x + x + x2 = 32 + -1x + -32 + x

Combine like terms: -31 + -32 = -63
-63 + x + x + x2 = 32 + -1x + -32 + x

Combine like terms: x + x = 2x
-63 + 2x + x2 = 32 + -1x + -32 + x

Reorder the terms:
-63 + 2x + x2 = 32 + -32 + -1x + x

Combine like terms: 32 + -32 = 0
-63 + 2x + x2 = 0 + -1x + x
-63 + 2x + x2 = -1x + x

Combine like terms: -1x + x = 0
-63 + 2x + x2 = 0

Factor a trinomial.
(-9 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-9, 7}