(12-2x)(16-2x)=96

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Solution for (12-2x)(16-2x)=96 equation: 


Simplifying
(12 + -2x)(16 + -2x) = 96

Multiply (12 + -2x) * (16 + -2x)
(12(16 + -2x) + -2x * (16 + -2x)) = 96
((16 * 12 + -2x * 12) + -2x * (16 + -2x)) = 96
((192 + -24x) + -2x * (16 + -2x)) = 96
(192 + -24x + (16 * -2x + -2x * -2x)) = 96
(192 + -24x + (-32x + 4x2)) = 96

Combine like terms: -24x + -32x = -56x
(192 + -56x + 4x2) = 96

Solving
192 + -56x + 4x2 = 96

Solving for variable 'x'.

Reorder the terms:
192 + -96 + -56x + 4x2 = 96 + -96

Combine like terms: 192 + -96 = 96
96 + -56x + 4x2 = 96 + -96

Combine like terms: 96 + -96 = 0
96 + -56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + -14x + x2) = 0

Factor a trinomial.
4((2 + -1x)(12 + -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 '(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 = {2, 12}

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