(6v^3-16v^2)(-21v-56)=0

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Solution for (6v^3-16v^2)(-21v-56)=0 equation: 


Simplifying
(6v3 + -16v2)(-21v + -56) = 0

Reorder the terms:
(-16v2 + 6v3)(-21v + -56) = 0

Reorder the terms:
(-16v2 + 6v3)(-56 + -21v) = 0

Multiply (-16v2 + 6v3) * (-56 + -21v)
(-16v2 * (-56 + -21v) + 6v3 * (-56 + -21v)) = 0
((-56 * -16v2 + -21v * -16v2) + 6v3 * (-56 + -21v)) = 0
((896v2 + 336v3) + 6v3 * (-56 + -21v)) = 0
(896v2 + 336v3 + (-56 * 6v3 + -21v * 6v3)) = 0
(896v2 + 336v3 + (-336v3 + -126v4)) = 0

Combine like terms: 336v3 + -336v3 = 0
(896v2 + 0 + -126v4) = 0
(896v2 + -126v4) = 0

Solving
896v2 + -126v4 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '14v2'.
14v2(64 + -9v2) = 0

Factor a difference between two squares.
14v2((8 + 3v)(8 + -3v)) = 0

Ignore the factor 14.

Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve:

Simplifying
v2 = 0

Solving
v2 = 0

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

Simplifying
v2 = 0

Take the square root of each side:
v = {0}

Subproblem 2
Set the factor '(8 + 3v)' equal to zero and attempt to solve:

Simplifying
8 + 3v = 0

Solving
8 + 3v = 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 + 3v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3v = 0 + -8
3v = 0 + -8

Combine like terms: 0 + -8 = -8
3v = -8

Divide each side by '3'.
v = -2.666666667

Simplifying
v = -2.666666667

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

Simplifying
8 + -3v = 0

Solving
8 + -3v = 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 + -3v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3v = 0 + -8
-3v = 0 + -8

Combine like terms: 0 + -8 = -8
-3v = -8

Divide each side by '-3'.
v = 2.666666667

Simplifying
v = 2.666666667
Solution
v = {0, -2.666666667, 2.666666667}

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