x^2-4x-50=2x+22

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Solution for x^2-4x-50=2x+22 equation: 


Simplifying
x2 + -4x + -50 = 2x + 22

Reorder the terms:
-50 + -4x + x2 = 2x + 22

Reorder the terms:
-50 + -4x + x2 = 22 + 2x

Solving
-50 + -4x + x2 = 22 + 2x

Solving for variable 'x'.

Reorder the terms:
-50 + -22 + -4x + -2x + x2 = 22 + 2x + -22 + -2x

Combine like terms: -50 + -22 = -72
-72 + -4x + -2x + x2 = 22 + 2x + -22 + -2x

Combine like terms: -4x + -2x = -6x
-72 + -6x + x2 = 22 + 2x + -22 + -2x

Reorder the terms:
-72 + -6x + x2 = 22 + -22 + 2x + -2x

Combine like terms: 22 + -22 = 0
-72 + -6x + x2 = 0 + 2x + -2x
-72 + -6x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-72 + -6x + x2 = 0

Factor a trinomial.
(-6 + -1x)(12 + -1x) = 0


Subproblem 1
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

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 = {-6, 12}

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