(12-2x)(9-2x)=54

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Solution for (12-2x)(9-2x)=54 equation: 


Simplifying
(12 + -2x)(9 + -2x) = 54

Multiply (12 + -2x) * (9 + -2x)
(12(9 + -2x) + -2x * (9 + -2x)) = 54
((9 * 12 + -2x * 12) + -2x * (9 + -2x)) = 54
((108 + -24x) + -2x * (9 + -2x)) = 54
(108 + -24x + (9 * -2x + -2x * -2x)) = 54
(108 + -24x + (-18x + 4x2)) = 54

Combine like terms: -24x + -18x = -42x
(108 + -42x + 4x2) = 54

Solving
108 + -42x + 4x2 = 54

Solving for variable 'x'.

Reorder the terms:
108 + -54 + -42x + 4x2 = 54 + -54

Combine like terms: 108 + -54 = 54
54 + -42x + 4x2 = 54 + -54

Combine like terms: 54 + -54 = 0
54 + -42x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + -21x + 2x2) = 0

Factor a trinomial.
2((3 + -2x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {1.5, 9}

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