x^2+12x-31=3x+5

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Solution for x^2+12x-31=3x+5 equation: 


Simplifying
x2 + 12x + -31 = 3x + 5

Reorder the terms:
-31 + 12x + x2 = 3x + 5

Reorder the terms:
-31 + 12x + x2 = 5 + 3x

Solving
-31 + 12x + x2 = 5 + 3x

Solving for variable 'x'.

Reorder the terms:
-31 + -5 + 12x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: -31 + -5 = -36
-36 + 12x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: 12x + -3x = 9x
-36 + 9x + x2 = 5 + 3x + -5 + -3x

Reorder the terms:
-36 + 9x + x2 = 5 + -5 + 3x + -3x

Combine like terms: 5 + -5 = 0
-36 + 9x + x2 = 0 + 3x + -3x
-36 + 9x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 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}

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