(14-2x)(12-2x)(x)=0

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Solution for (14-2x)(12-2x)(x)=0 equation: 


Simplifying
(14 + -2x)(12 + -2x)(x) = 0

Reorder the terms for easier multiplication:
x(14 + -2x)(12 + -2x) = 0

Multiply (14 + -2x) * (12 + -2x)
x(14(12 + -2x) + -2x * (12 + -2x)) = 0
x((12 * 14 + -2x * 14) + -2x * (12 + -2x)) = 0
x((168 + -28x) + -2x * (12 + -2x)) = 0
x(168 + -28x + (12 * -2x + -2x * -2x)) = 0
x(168 + -28x + (-24x + 4x2)) = 0

Combine like terms: -28x + -24x = -52x
x(168 + -52x + 4x2) = 0
(168 * x + -52x * x + 4x2 * x) = 0
(168x + -52x2 + 4x3) = 0

Solving
168x + -52x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(42 + -13x + x2) = 0

Factor a trinomial.
4x((6 + -1x)(7 + -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 '(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

Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0, 6, 7}

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