(12-2x)(12-4x)=54

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Solution for (12-2x)(12-4x)=54 equation: 


Simplifying
(12 + -2x)(12 + -4x) = 54

Multiply (12 + -2x) * (12 + -4x)
(12(12 + -4x) + -2x * (12 + -4x)) = 54
((12 * 12 + -4x * 12) + -2x * (12 + -4x)) = 54
((144 + -48x) + -2x * (12 + -4x)) = 54
(144 + -48x + (12 * -2x + -4x * -2x)) = 54
(144 + -48x + (-24x + 8x2)) = 54

Combine like terms: -48x + -24x = -72x
(144 + -72x + 8x2) = 54

Solving
144 + -72x + 8x2 = 54

Solving for variable 'x'.

Reorder the terms:
144 + -54 + -72x + 8x2 = 54 + -54

Combine like terms: 144 + -54 = 90
90 + -72x + 8x2 = 54 + -54

Combine like terms: 54 + -54 = 0
90 + -72x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + -36x + 4x2) = 0

Factor a trinomial.
2((3 + -2x)(15 + -2x)) = 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 '(15 + -2x)' equal to zero and attempt to solve:

Simplifying
15 + -2x = 0

Solving
15 + -2x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2x = 0 + -15
-2x = 0 + -15

Combine like terms: 0 + -15 = -15
-2x = -15

Divide each side by '-2'.
x = 7.5

Simplifying
x = 7.5
Solution
x = {1.5, 7.5}

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