(7-x)(32x+16x)(4x-8)=0

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Solution for (7-x)(32x+16x)(4x-8)=0 equation: 


Simplifying
(7 + -1x)(32x + 16x)(4x + -8) = 0

Combine like terms: 32x + 16x = 48x
(7 + -1x)(48x)(4x + -8) = 0

Remove parenthesis around (48x)
(7 + -1x) * 48x(4x + -8) = 0

Reorder the terms:
(7 + -1x) * 48x(-8 + 4x) = 0

Reorder the terms for easier multiplication:
48x(7 + -1x)(-8 + 4x) = 0

Multiply (7 + -1x) * (-8 + 4x)
48x(7(-8 + 4x) + -1x * (-8 + 4x)) = 0
48x((-8 * 7 + 4x * 7) + -1x * (-8 + 4x)) = 0
48x((-56 + 28x) + -1x * (-8 + 4x)) = 0
48x(-56 + 28x + (-8 * -1x + 4x * -1x)) = 0
48x(-56 + 28x + (8x + -4x2)) = 0

Combine like terms: 28x + 8x = 36x
48x(-56 + 36x + -4x2) = 0
(-56 * 48x + 36x * 48x + -4x2 * 48x) = 0
(-2688x + 1728x2 + -192x3) = 0

Solving
-2688x + 1728x2 + -192x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '192x'.
192x(-14 + 9x + -1x2) = 0

Factor a trinomial.
192x((-7 + x)(2 + -1x)) = 0

Ignore the factor 192.

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 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 7, 2}

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