=x(16-2x)(21-2x)

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Solution for =x(16-2x)(21-2x) equation: 


Simplifying
0 = x(16 + -2x)(21 + -2x)

Multiply (16 + -2x) * (21 + -2x)
0 = x(16(21 + -2x) + -2x * (21 + -2x))
0 = x((21 * 16 + -2x * 16) + -2x * (21 + -2x))
0 = x((336 + -32x) + -2x * (21 + -2x))
0 = x(336 + -32x + (21 * -2x + -2x * -2x))
0 = x(336 + -32x + (-42x + 4x2))

Combine like terms: -32x + -42x = -74x
0 = x(336 + -74x + 4x2)
0 = (336 * x + -74x * x + 4x2 * x)
0 = (336x + -74x2 + 4x3)

Solving
0 = 336x + -74x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-336x + 74x2 + -4x3 = 336x + -74x2 + 4x3 + -336x + 74x2 + -4x3

Reorder the terms:
-336x + 74x2 + -4x3 = 336x + -336x + -74x2 + 74x2 + 4x3 + -4x3

Combine like terms: 336x + -336x = 0
-336x + 74x2 + -4x3 = 0 + -74x2 + 74x2 + 4x3 + -4x3
-336x + 74x2 + -4x3 = -74x2 + 74x2 + 4x3 + -4x3

Combine like terms: -74x2 + 74x2 = 0
-336x + 74x2 + -4x3 = 0 + 4x3 + -4x3
-336x + 74x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-336x + 74x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-168 + 37x + -2x2) = 0

Factor a trinomial.
2x((-21 + 2x)(8 + -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 '(-21 + 2x)' equal to zero and attempt to solve:

Simplifying
-21 + 2x = 0

Solving
-21 + 2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + 2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2x = 0 + 21
2x = 0 + 21

Combine like terms: 0 + 21 = 21
2x = 21

Divide each side by '2'.
x = 10.5

Simplifying
x = 10.5

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, 10.5, 8}

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