-4v(v-6)(v-7)=0

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Solution for -4v(v-6)(v-7)=0 equation: 


Simplifying
-4v(v + -6)(v + -7) = 0

Reorder the terms:
-4v(-6 + v)(v + -7) = 0

Reorder the terms:
-4v(-6 + v)(-7 + v) = 0

Multiply (-6 + v) * (-7 + v)
-4v(-6(-7 + v) + v(-7 + v)) = 0
-4v((-7 * -6 + v * -6) + v(-7 + v)) = 0
-4v((42 + -6v) + v(-7 + v)) = 0
-4v(42 + -6v + (-7 * v + v * v)) = 0
-4v(42 + -6v + (-7v + v2)) = 0

Combine like terms: -6v + -7v = -13v
-4v(42 + -13v + v2) = 0
(42 * -4v + -13v * -4v + v2 * -4v) = 0
(-168v + 52v2 + -4v3) = 0

Solving
-168v + 52v2 + -4v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4v'.
4v(-42 + 13v + -1v2) = 0

Factor a trinomial.
4v((-7 + v)(6 + -1v)) = 0

Ignore the factor 4.

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 '(-7 + v)' equal to zero and attempt to solve:

Simplifying
-7 + v = 0

Solving
-7 + v = 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 + v = 0 + 7

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

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

Simplifying
v = 7

Subproblem 3
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Solution
v = {0, 7, 6}

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