(24-2x)(14-2x)(x)=0

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Solution for (24-2x)(14-2x)(x)=0 equation:


Simplifying
(24 + -2x)(14 + -2x)(x) = 0

Reorder the terms for easier multiplication:
x(24 + -2x)(14 + -2x) = 0

Multiply (24 + -2x) * (14 + -2x)
x(24(14 + -2x) + -2x * (14 + -2x)) = 0
x((14 * 24 + -2x * 24) + -2x * (14 + -2x)) = 0
x((336 + -48x) + -2x * (14 + -2x)) = 0
x(336 + -48x + (14 * -2x + -2x * -2x)) = 0
x(336 + -48x + (-28x + 4x2)) = 0

Combine like terms: -48x + -28x = -76x
x(336 + -76x + 4x2) = 0
(336 * x + -76x * x + 4x2 * x) = 0
(336x + -76x2 + 4x3) = 0

Solving
336x + -76x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(84 + -19x + x2) = 0

Factor a trinomial.
4x((7 + -1x)(12 + -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 '(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

Subproblem 3
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {0, 7, 12}

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