x^2-12x+32=2x-16

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Solution for x^2-12x+32=2x-16 equation: 


Simplifying
x2 + -12x + 32 = 2x + -16

Reorder the terms:
32 + -12x + x2 = 2x + -16

Reorder the terms:
32 + -12x + x2 = -16 + 2x

Solving
32 + -12x + x2 = -16 + 2x

Solving for variable 'x'.

Reorder the terms:
32 + 16 + -12x + -2x + x2 = -16 + 2x + 16 + -2x

Combine like terms: 32 + 16 = 48
48 + -12x + -2x + x2 = -16 + 2x + 16 + -2x

Combine like terms: -12x + -2x = -14x
48 + -14x + x2 = -16 + 2x + 16 + -2x

Reorder the terms:
48 + -14x + x2 = -16 + 16 + 2x + -2x

Combine like terms: -16 + 16 = 0
48 + -14x + x2 = 0 + 2x + -2x
48 + -14x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
48 + -14x + x2 = 0

Factor a trinomial.
(6 + -1x)(8 + -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 '(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 = {6, 8}

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