x^2-2x-19=2x+13

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Solution for x^2-2x-19=2x+13 equation: 


Simplifying
x2 + -2x + -19 = 2x + 13

Reorder the terms:
-19 + -2x + x2 = 2x + 13

Reorder the terms:
-19 + -2x + x2 = 13 + 2x

Solving
-19 + -2x + x2 = 13 + 2x

Solving for variable 'x'.

Reorder the terms:
-19 + -13 + -2x + -2x + x2 = 13 + 2x + -13 + -2x

Combine like terms: -19 + -13 = -32
-32 + -2x + -2x + x2 = 13 + 2x + -13 + -2x

Combine like terms: -2x + -2x = -4x
-32 + -4x + x2 = 13 + 2x + -13 + -2x

Reorder the terms:
-32 + -4x + x2 = 13 + -13 + 2x + -2x

Combine like terms: 13 + -13 = 0
-32 + -4x + x2 = 0 + 2x + -2x
-32 + -4x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-32 + -4x + x2 = 0

Factor a trinomial.
(-4 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-4, 8}

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