x^2-14x+31=-4x+7

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Solution for x^2-14x+31=-4x+7 equation: 


Simplifying
x2 + -14x + 31 = -4x + 7

Reorder the terms:
31 + -14x + x2 = -4x + 7

Reorder the terms:
31 + -14x + x2 = 7 + -4x

Solving
31 + -14x + x2 = 7 + -4x

Solving for variable 'x'.

Reorder the terms:
31 + -7 + -14x + 4x + x2 = 7 + -4x + -7 + 4x

Combine like terms: 31 + -7 = 24
24 + -14x + 4x + x2 = 7 + -4x + -7 + 4x

Combine like terms: -14x + 4x = -10x
24 + -10x + x2 = 7 + -4x + -7 + 4x

Reorder the terms:
24 + -10x + x2 = 7 + -7 + -4x + 4x

Combine like terms: 7 + -7 = 0
24 + -10x + x2 = 0 + -4x + 4x
24 + -10x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
24 + -10x + x2 = 0

Factor a trinomial.
(4 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {4, 6}

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