(12-2x)(8-2x)=32

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Solution for (12-2x)(8-2x)=32 equation: 


Simplifying
(12 + -2x)(8 + -2x) = 32

Multiply (12 + -2x) * (8 + -2x)
(12(8 + -2x) + -2x * (8 + -2x)) = 32
((8 * 12 + -2x * 12) + -2x * (8 + -2x)) = 32
((96 + -24x) + -2x * (8 + -2x)) = 32
(96 + -24x + (8 * -2x + -2x * -2x)) = 32
(96 + -24x + (-16x + 4x2)) = 32

Combine like terms: -24x + -16x = -40x
(96 + -40x + 4x2) = 32

Solving
96 + -40x + 4x2 = 32

Solving for variable 'x'.

Reorder the terms:
96 + -32 + -40x + 4x2 = 32 + -32

Combine like terms: 96 + -32 = 64
64 + -40x + 4x2 = 32 + -32

Combine like terms: 32 + -32 = 0
64 + -40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -10x + x2) = 0

Factor a trinomial.
4((2 + -1x)(8 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 8}

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