-3v(4v-18)(v+12)=0

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Solution for -3v(4v-18)(v+12)=0 equation: 


Simplifying
-3v(4v + -18)(v + 12) = 0

Reorder the terms:
-3v(-18 + 4v)(v + 12) = 0

Reorder the terms:
-3v(-18 + 4v)(12 + v) = 0

Multiply (-18 + 4v) * (12 + v)
-3v(-18(12 + v) + 4v * (12 + v)) = 0
-3v((12 * -18 + v * -18) + 4v * (12 + v)) = 0
-3v((-216 + -18v) + 4v * (12 + v)) = 0
-3v(-216 + -18v + (12 * 4v + v * 4v)) = 0
-3v(-216 + -18v + (48v + 4v2)) = 0

Combine like terms: -18v + 48v = 30v
-3v(-216 + 30v + 4v2) = 0
(-216 * -3v + 30v * -3v + 4v2 * -3v) = 0
(648v + -90v2 + -12v3) = 0

Solving
648v + -90v2 + -12v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '6v'.
6v(108 + -15v + -2v2) = 0

Factor a trinomial.
6v((9 + -2v)(12 + v)) = 0

Ignore the factor 6.

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 '(9 + -2v)' equal to zero and attempt to solve:

Simplifying
9 + -2v = 0

Solving
9 + -2v = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2v = 0 + -9
-2v = 0 + -9

Combine like terms: 0 + -9 = -9
-2v = -9

Divide each side by '-2'.
v = 4.5

Simplifying
v = 4.5

Subproblem 3
Set the factor '(12 + v)' equal to zero and attempt to solve:

Simplifying
12 + v = 0

Solving
12 + v = 0

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

Add '-12' to each side of the equation.
12 + -12 + v = 0 + -12

Combine like terms: 12 + -12 = 0
0 + v = 0 + -12
v = 0 + -12

Combine like terms: 0 + -12 = -12
v = -12

Simplifying
v = -12
Solution
v = {0, 4.5, -12}

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