x^2-17x+31=-2x-5

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Solution for x^2-17x+31=-2x-5 equation: 


Simplifying
x2 + -17x + 31 = -2x + -5

Reorder the terms:
31 + -17x + x2 = -2x + -5

Reorder the terms:
31 + -17x + x2 = -5 + -2x

Solving
31 + -17x + x2 = -5 + -2x

Solving for variable 'x'.

Reorder the terms:
31 + 5 + -17x + 2x + x2 = -5 + -2x + 5 + 2x

Combine like terms: 31 + 5 = 36
36 + -17x + 2x + x2 = -5 + -2x + 5 + 2x

Combine like terms: -17x + 2x = -15x
36 + -15x + x2 = -5 + -2x + 5 + 2x

Reorder the terms:
36 + -15x + x2 = -5 + 5 + -2x + 2x

Combine like terms: -5 + 5 = 0
36 + -15x + x2 = 0 + -2x + 2x
36 + -15x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
36 + -15x + x2 = 0

Factor a trinomial.
(3 + -1x)(12 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {3, 12}

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