x^2-19x+31=-6x-5

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Solution for x^2-19x+31=-6x-5 equation: 


Simplifying
x2 + -19x + 31 = -6x + -5

Reorder the terms:
31 + -19x + x2 = -6x + -5

Reorder the terms:
31 + -19x + x2 = -5 + -6x

Solving
31 + -19x + x2 = -5 + -6x

Solving for variable 'x'.

Reorder the terms:
31 + 5 + -19x + 6x + x2 = -5 + -6x + 5 + 6x

Combine like terms: 31 + 5 = 36
36 + -19x + 6x + x2 = -5 + -6x + 5 + 6x

Combine like terms: -19x + 6x = -13x
36 + -13x + x2 = -5 + -6x + 5 + 6x

Reorder the terms:
36 + -13x + x2 = -5 + 5 + -6x + 6x

Combine like terms: -5 + 5 = 0
36 + -13x + x2 = 0 + -6x + 6x
36 + -13x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
36 + -13x + 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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