3v(v+4)(v-7)=0

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Solution for 3v(v+4)(v-7)=0 equation: 


Simplifying
3v(v + 4)(v + -7) = 0

Reorder the terms:
3v(4 + v)(v + -7) = 0

Reorder the terms:
3v(4 + v)(-7 + v) = 0

Multiply (4 + v) * (-7 + v)
3v(4(-7 + v) + v(-7 + v)) = 0
3v((-7 * 4 + v * 4) + v(-7 + v)) = 0
3v((-28 + 4v) + v(-7 + v)) = 0
3v(-28 + 4v + (-7 * v + v * v)) = 0
3v(-28 + 4v + (-7v + v2)) = 0

Combine like terms: 4v + -7v = -3v
3v(-28 + -3v + v2) = 0
(-28 * 3v + -3v * 3v + v2 * 3v) = 0
(-84v + -9v2 + 3v3) = 0

Solving
-84v + -9v2 + 3v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3v'.
3v(-28 + -3v + v2) = 0

Factor a trinomial.
3v((-4 + -1v)(7 + -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 '(-4 + -1v)' equal to zero and attempt to solve:

Simplifying
-4 + -1v = 0

Solving
-4 + -1v = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1v = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1v = 0 + 4
-1v = 0 + 4

Combine like terms: 0 + 4 = 4
-1v = 4

Divide each side by '-1'.
v = -4

Simplifying
v = -4

Subproblem 3
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {0, -4, 7}

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