x^2-x-31=4x+5

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Solution for x^2-x-31=4x+5 equation: 


Simplifying
x2 + -1x + -31 = 4x + 5

Reorder the terms:
-31 + -1x + x2 = 4x + 5

Reorder the terms:
-31 + -1x + x2 = 5 + 4x

Solving
-31 + -1x + x2 = 5 + 4x

Solving for variable 'x'.

Reorder the terms:
-31 + -5 + -1x + -4x + x2 = 5 + 4x + -5 + -4x

Combine like terms: -31 + -5 = -36
-36 + -1x + -4x + x2 = 5 + 4x + -5 + -4x

Combine like terms: -1x + -4x = -5x
-36 + -5x + x2 = 5 + 4x + -5 + -4x

Reorder the terms:
-36 + -5x + x2 = 5 + -5 + 4x + -4x

Combine like terms: 5 + -5 = 0
-36 + -5x + x2 = 0 + 4x + -4x
-36 + -5x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-36 + -5x + x2 = 0

Factor a trinomial.
(-4 + -1x)(9 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-4, 9}

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