(12-2x)(15-2x)=108

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Solution for (12-2x)(15-2x)=108 equation: 


Simplifying
(12 + -2x)(15 + -2x) = 108

Multiply (12 + -2x) * (15 + -2x)
(12(15 + -2x) + -2x * (15 + -2x)) = 108
((15 * 12 + -2x * 12) + -2x * (15 + -2x)) = 108
((180 + -24x) + -2x * (15 + -2x)) = 108
(180 + -24x + (15 * -2x + -2x * -2x)) = 108
(180 + -24x + (-30x + 4x2)) = 108

Combine like terms: -24x + -30x = -54x
(180 + -54x + 4x2) = 108

Solving
180 + -54x + 4x2 = 108

Solving for variable 'x'.

Reorder the terms:
180 + -108 + -54x + 4x2 = 108 + -108

Combine like terms: 180 + -108 = 72
72 + -54x + 4x2 = 108 + -108

Combine like terms: 108 + -108 = 0
72 + -54x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -27x + 2x2) = 0

Factor a trinomial.
2((3 + -2x)(12 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

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 = {1.5, 12}

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