=x(24-2x)(24-2x)

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


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

Multiply (24 + -2x) * (24 + -2x)
0 = x(24(24 + -2x) + -2x * (24 + -2x))
0 = x((24 * 24 + -2x * 24) + -2x * (24 + -2x))
0 = x((576 + -48x) + -2x * (24 + -2x))
0 = x(576 + -48x + (24 * -2x + -2x * -2x))
0 = x(576 + -48x + (-48x + 4x2))

Combine like terms: -48x + -48x = -96x
0 = x(576 + -96x + 4x2)
0 = (576 * x + -96x * x + 4x2 * x)
0 = (576x + -96x2 + 4x3)

Solving
0 = 576x + -96x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-576x + 96x2 + -4x3 = 576x + -96x2 + 4x3 + -576x + 96x2 + -4x3

Reorder the terms:
-576x + 96x2 + -4x3 = 576x + -576x + -96x2 + 96x2 + 4x3 + -4x3

Combine like terms: 576x + -576x = 0
-576x + 96x2 + -4x3 = 0 + -96x2 + 96x2 + 4x3 + -4x3
-576x + 96x2 + -4x3 = -96x2 + 96x2 + 4x3 + -4x3

Combine like terms: -96x2 + 96x2 = 0
-576x + 96x2 + -4x3 = 0 + 4x3 + -4x3
-576x + 96x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-576x + 96x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-144 + 24x + -1x2) = 0

Factor a trinomial.
4x((-12 + x)(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 '(-12 + x)' equal to zero and attempt to solve:

Simplifying
-12 + x = 0

Solving
-12 + x = 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 + x = 0 + 12

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

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

Simplifying
x = 12

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, 12, 12}

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