(50-2x)*(24-2x)*x=360x

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Solution for (50-2x)*(24-2x)*x=360x equation: 


Simplifying
(50 + -2x)(24 + -2x) * x = 360x

Reorder the terms for easier multiplication:
x(50 + -2x)(24 + -2x) = 360x

Multiply (50 + -2x) * (24 + -2x)
x(50(24 + -2x) + -2x * (24 + -2x)) = 360x
x((24 * 50 + -2x * 50) + -2x * (24 + -2x)) = 360x
x((1200 + -100x) + -2x * (24 + -2x)) = 360x
x(1200 + -100x + (24 * -2x + -2x * -2x)) = 360x
x(1200 + -100x + (-48x + 4x2)) = 360x

Combine like terms: -100x + -48x = -148x
x(1200 + -148x + 4x2) = 360x
(1200 * x + -148x * x + 4x2 * x) = 360x
(1200x + -148x2 + 4x3) = 360x

Solving
1200x + -148x2 + 4x3 = 360x

Solving for variable 'x'.

Reorder the terms:
1200x + -360x + -148x2 + 4x3 = 360x + -360x

Combine like terms: 1200x + -360x = 840x
840x + -148x2 + 4x3 = 360x + -360x

Combine like terms: 360x + -360x = 0
840x + -148x2 + 4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(210 + -37x + x2) = 0

Factor a trinomial.
4x((7 + -1x)(30 + -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 '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {0, 7, 30}

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