0=(80-2x)(50-2x)(x)

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Solution for 0=(80-2x)(50-2x)(x) equation: 


Simplifying
0 = (80 + -2x)(50 + -2x)(x)

Reorder the terms for easier multiplication:
0 = x(80 + -2x)(50 + -2x)

Multiply (80 + -2x) * (50 + -2x)
0 = x(80(50 + -2x) + -2x * (50 + -2x))
0 = x((50 * 80 + -2x * 80) + -2x * (50 + -2x))
0 = x((4000 + -160x) + -2x * (50 + -2x))
0 = x(4000 + -160x + (50 * -2x + -2x * -2x))
0 = x(4000 + -160x + (-100x + 4x2))

Combine like terms: -160x + -100x = -260x
0 = x(4000 + -260x + 4x2)
0 = (4000 * x + -260x * x + 4x2 * x)
0 = (4000x + -260x2 + 4x3)

Solving
0 = 4000x + -260x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-4000x + 260x2 + -4x3 = 4000x + -260x2 + 4x3 + -4000x + 260x2 + -4x3

Reorder the terms:
-4000x + 260x2 + -4x3 = 4000x + -4000x + -260x2 + 260x2 + 4x3 + -4x3

Combine like terms: 4000x + -4000x = 0
-4000x + 260x2 + -4x3 = 0 + -260x2 + 260x2 + 4x3 + -4x3
-4000x + 260x2 + -4x3 = -260x2 + 260x2 + 4x3 + -4x3

Combine like terms: -260x2 + 260x2 = 0
-4000x + 260x2 + -4x3 = 0 + 4x3 + -4x3
-4000x + 260x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-4000x + 260x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-1000 + 65x + -1x2) = 0

Factor a trinomial.
4x((-40 + x)(25 + -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 '(-40 + x)' equal to zero and attempt to solve:

Simplifying
-40 + x = 0

Solving
-40 + x = 0

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

Add '40' to each side of the equation.
-40 + 40 + x = 0 + 40

Combine like terms: -40 + 40 = 0
0 + x = 0 + 40
x = 0 + 40

Combine like terms: 0 + 40 = 40
x = 40

Simplifying
x = 40

Subproblem 3
Set the factor '(25 + -1x)' equal to zero and attempt to solve:

Simplifying
25 + -1x = 0

Solving
25 + -1x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 0 + -25
-1x = 0 + -25

Combine like terms: 0 + -25 = -25
-1x = -25

Divide each side by '-1'.
x = 25

Simplifying
x = 25
Solution
x = {0, 40, 25}

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