(12-2x)(9-2x)(x)=0

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Solution for (12-2x)(9-2x)(x)=0 equation: 


Simplifying
(12 + -2x)(9 + -2x)(x) = 0

Reorder the terms for easier multiplication:
x(12 + -2x)(9 + -2x) = 0

Multiply (12 + -2x) * (9 + -2x)
x(12(9 + -2x) + -2x * (9 + -2x)) = 0
x((9 * 12 + -2x * 12) + -2x * (9 + -2x)) = 0
x((108 + -24x) + -2x * (9 + -2x)) = 0
x(108 + -24x + (9 * -2x + -2x * -2x)) = 0
x(108 + -24x + (-18x + 4x2)) = 0

Combine like terms: -24x + -18x = -42x
x(108 + -42x + 4x2) = 0
(108 * x + -42x * x + 4x2 * x) = 0
(108x + -42x2 + 4x3) = 0

Solving
108x + -42x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(54 + -21x + 2x2) = 0

Factor a trinomial.
2x((9 + -2x)(6 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5

Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 4.5, 6}

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