0=(30-2x)(16-2x)x

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Solution for 0=(30-2x)(16-2x)x equation: 


Simplifying
0 = (30 + -2x)(16 + -2x) * x

Reorder the terms for easier multiplication:
0 = x(30 + -2x)(16 + -2x)

Multiply (30 + -2x) * (16 + -2x)
0 = x(30(16 + -2x) + -2x * (16 + -2x))
0 = x((16 * 30 + -2x * 30) + -2x * (16 + -2x))
0 = x((480 + -60x) + -2x * (16 + -2x))
0 = x(480 + -60x + (16 * -2x + -2x * -2x))
0 = x(480 + -60x + (-32x + 4x2))

Combine like terms: -60x + -32x = -92x
0 = x(480 + -92x + 4x2)
0 = (480 * x + -92x * x + 4x2 * x)
0 = (480x + -92x2 + 4x3)

Solving
0 = 480x + -92x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-480x + 92x2 + -4x3 = 480x + -92x2 + 4x3 + -480x + 92x2 + -4x3

Reorder the terms:
-480x + 92x2 + -4x3 = 480x + -480x + -92x2 + 92x2 + 4x3 + -4x3

Combine like terms: 480x + -480x = 0
-480x + 92x2 + -4x3 = 0 + -92x2 + 92x2 + 4x3 + -4x3
-480x + 92x2 + -4x3 = -92x2 + 92x2 + 4x3 + -4x3

Combine like terms: -92x2 + 92x2 = 0
-480x + 92x2 + -4x3 = 0 + 4x3 + -4x3
-480x + 92x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-480x + 92x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-120 + 23x + -1x2) = 0

Factor a trinomial.
4x((-15 + x)(8 + -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 '(-15 + x)' equal to zero and attempt to solve:

Simplifying
-15 + x = 0

Solving
-15 + x = 0

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

Add '15' to each side of the equation.
-15 + 15 + x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + x = 0 + 15
x = 0 + 15

Combine like terms: 0 + 15 = 15
x = 15

Simplifying
x = 15

Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 15, 8}

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