3v(v-7)(v-2)=0

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Solution for 3v(v-7)(v-2)=0 equation: 


Simplifying
3v(v + -7)(v + -2) = 0

Reorder the terms:
3v(-7 + v)(v + -2) = 0

Reorder the terms:
3v(-7 + v)(-2 + v) = 0

Multiply (-7 + v) * (-2 + v)
3v(-7(-2 + v) + v(-2 + v)) = 0
3v((-2 * -7 + v * -7) + v(-2 + v)) = 0
3v((14 + -7v) + v(-2 + v)) = 0
3v(14 + -7v + (-2 * v + v * v)) = 0
3v(14 + -7v + (-2v + v2)) = 0

Combine like terms: -7v + -2v = -9v
3v(14 + -9v + v2) = 0
(14 * 3v + -9v * 3v + v2 * 3v) = 0
(42v + -27v2 + 3v3) = 0

Solving
42v + -27v2 + 3v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3v'.
3v(14 + -9v + v2) = 0

Factor a trinomial.
3v((2 + -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 '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2

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, 2, 7}

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