x(12-2x)(10-2x)=0

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Solution for x(12-2x)(10-2x)=0 equation: 


Simplifying
x(12 + -2x)(10 + -2x) = 0

Multiply (12 + -2x) * (10 + -2x)
x(12(10 + -2x) + -2x * (10 + -2x)) = 0
x((10 * 12 + -2x * 12) + -2x * (10 + -2x)) = 0
x((120 + -24x) + -2x * (10 + -2x)) = 0
x(120 + -24x + (10 * -2x + -2x * -2x)) = 0
x(120 + -24x + (-20x + 4x2)) = 0

Combine like terms: -24x + -20x = -44x
x(120 + -44x + 4x2) = 0
(120 * x + -44x * x + 4x2 * x) = 0
(120x + -44x2 + 4x3) = 0

Solving
120x + -44x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(30 + -11x + x2) = 0

Factor a trinomial.
4x((5 + -1x)(6 + -1x)) = 0

Ignore the factor 4.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 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, 5, 6}

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