0=(60-2x)(40-2x)(x)

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Solution for 0=(60-2x)(40-2x)(x) equation: 


Simplifying
0 = (60 + -2x)(40 + -2x)(x)

Reorder the terms for easier multiplication:
0 = x(60 + -2x)(40 + -2x)

Multiply (60 + -2x) * (40 + -2x)
0 = x(60(40 + -2x) + -2x * (40 + -2x))
0 = x((40 * 60 + -2x * 60) + -2x * (40 + -2x))
0 = x((2400 + -120x) + -2x * (40 + -2x))
0 = x(2400 + -120x + (40 * -2x + -2x * -2x))
0 = x(2400 + -120x + (-80x + 4x2))

Combine like terms: -120x + -80x = -200x
0 = x(2400 + -200x + 4x2)
0 = (2400 * x + -200x * x + 4x2 * x)
0 = (2400x + -200x2 + 4x3)

Solving
0 = 2400x + -200x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-2400x + 200x2 + -4x3 = 2400x + -200x2 + 4x3 + -2400x + 200x2 + -4x3

Reorder the terms:
-2400x + 200x2 + -4x3 = 2400x + -2400x + -200x2 + 200x2 + 4x3 + -4x3

Combine like terms: 2400x + -2400x = 0
-2400x + 200x2 + -4x3 = 0 + -200x2 + 200x2 + 4x3 + -4x3
-2400x + 200x2 + -4x3 = -200x2 + 200x2 + 4x3 + -4x3

Combine like terms: -200x2 + 200x2 = 0
-2400x + 200x2 + -4x3 = 0 + 4x3 + -4x3
-2400x + 200x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-2400x + 200x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-600 + 50x + -1x2) = 0

Factor a trinomial.
4x((-30 + x)(20 + -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 '(-30 + x)' equal to zero and attempt to solve:

Simplifying
-30 + x = 0

Solving
-30 + x = 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 + x = 0 + 30

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

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

Simplifying
x = 30

Subproblem 3
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {0, 30, 20}

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