=x(24-2x)(45-2x)

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Solution for =x(24-2x)(45-2x) equation: 


Simplifying
0 = x(24 + -2x)(45 + -2x)

Multiply (24 + -2x) * (45 + -2x)
0 = x(24(45 + -2x) + -2x * (45 + -2x))
0 = x((45 * 24 + -2x * 24) + -2x * (45 + -2x))
0 = x((1080 + -48x) + -2x * (45 + -2x))
0 = x(1080 + -48x + (45 * -2x + -2x * -2x))
0 = x(1080 + -48x + (-90x + 4x2))

Combine like terms: -48x + -90x = -138x
0 = x(1080 + -138x + 4x2)
0 = (1080 * x + -138x * x + 4x2 * x)
0 = (1080x + -138x2 + 4x3)

Solving
0 = 1080x + -138x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-1080x + 138x2 + -4x3 = 1080x + -138x2 + 4x3 + -1080x + 138x2 + -4x3

Reorder the terms:
-1080x + 138x2 + -4x3 = 1080x + -1080x + -138x2 + 138x2 + 4x3 + -4x3

Combine like terms: 1080x + -1080x = 0
-1080x + 138x2 + -4x3 = 0 + -138x2 + 138x2 + 4x3 + -4x3
-1080x + 138x2 + -4x3 = -138x2 + 138x2 + 4x3 + -4x3

Combine like terms: -138x2 + 138x2 = 0
-1080x + 138x2 + -4x3 = 0 + 4x3 + -4x3
-1080x + 138x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-1080x + 138x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-540 + 69x + -2x2) = 0

Factor a trinomial.
2x((-45 + 2x)(12 + -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 '(-45 + 2x)' equal to zero and attempt to solve:

Simplifying
-45 + 2x = 0

Solving
-45 + 2x = 0

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

Add '45' to each side of the equation.
-45 + 45 + 2x = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 2x = 0 + 45
2x = 0 + 45

Combine like terms: 0 + 45 = 45
2x = 45

Divide each side by '2'.
x = 22.5

Simplifying
x = 22.5

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, 22.5, 12}

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