2v^2(v-6)=32v

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Solution for 2v^2(v-6)=32v equation: 


Simplifying
2v2(v + -6) = 32v

Reorder the terms:
2v2(-6 + v) = 32v
(-6 * 2v2 + v * 2v2) = 32v
(-12v2 + 2v3) = 32v

Solving
-12v2 + 2v3 = 32v

Solving for variable 'v'.

Reorder the terms:
-32v + -12v2 + 2v3 = 32v + -32v

Combine like terms: 32v + -32v = 0
-32v + -12v2 + 2v3 = 0

Factor out the Greatest Common Factor (GCF), '2v'.
2v(-16 + -6v + v2) = 0

Factor a trinomial.
2v((-2 + -1v)(8 + -1v)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'v' equal to zero and attempt to solve:

Simplifying
v = 0

Solving
v = 0

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

Simplifying
v = 0

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

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

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

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

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

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

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

Simplifying
v = -2

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

Simplifying
8 + -1v = 0

Solving
8 + -1v = 0

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

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

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

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

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

Simplifying
v = 8
Solution
v = {0, -2, 8}

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