3v(v+5)(v-9)=0

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Solution for 3v(v+5)(v-9)=0 equation: 


Simplifying
3v(v + 5)(v + -9) = 0

Reorder the terms:
3v(5 + v)(v + -9) = 0

Reorder the terms:
3v(5 + v)(-9 + v) = 0

Multiply (5 + v) * (-9 + v)
3v(5(-9 + v) + v(-9 + v)) = 0
3v((-9 * 5 + v * 5) + v(-9 + v)) = 0
3v((-45 + 5v) + v(-9 + v)) = 0
3v(-45 + 5v + (-9 * v + v * v)) = 0
3v(-45 + 5v + (-9v + v2)) = 0

Combine like terms: 5v + -9v = -4v
3v(-45 + -4v + v2) = 0
(-45 * 3v + -4v * 3v + v2 * 3v) = 0
(-135v + -12v2 + 3v3) = 0

Solving
-135v + -12v2 + 3v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3v'.
3v(-45 + -4v + v2) = 0

Factor a trinomial.
3v((-5 + -1v)(9 + -1v)) = 0

Ignore the factor 3.

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 '(-5 + -1v)' equal to zero and attempt to solve:

Simplifying
-5 + -1v = 0

Solving
-5 + -1v = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1v = 0 + 5
-1v = 0 + 5

Combine like terms: 0 + 5 = 5
-1v = 5

Divide each side by '-1'.
v = -5

Simplifying
v = -5

Subproblem 3
Set the factor '(9 + -1v)' equal to zero and attempt to solve:

Simplifying
9 + -1v = 0

Solving
9 + -1v = 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 + -1v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1v = 0 + -9
-1v = 0 + -9

Combine like terms: 0 + -9 = -9
-1v = -9

Divide each side by '-1'.
v = 9

Simplifying
v = 9
Solution
v = {0, -5, 9}

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