4v(v-1)(v-2)=0

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Solution for 4v(v-1)(v-2)=0 equation: 


Simplifying
4v(v + -1)(v + -2) = 0

Reorder the terms:
4v(-1 + v)(v + -2) = 0

Reorder the terms:
4v(-1 + v)(-2 + v) = 0

Multiply (-1 + v) * (-2 + v)
4v(-1(-2 + v) + v(-2 + v)) = 0
4v((-2 * -1 + v * -1) + v(-2 + v)) = 0
4v((2 + -1v) + v(-2 + v)) = 0
4v(2 + -1v + (-2 * v + v * v)) = 0
4v(2 + -1v + (-2v + v2)) = 0

Combine like terms: -1v + -2v = -3v
4v(2 + -3v + v2) = 0
(2 * 4v + -3v * 4v + v2 * 4v) = 0
(8v + -12v2 + 4v3) = 0

Solving
8v + -12v2 + 4v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4v'.
4v(2 + -3v + v2) = 0

Factor a trinomial.
4v((1 + -1v)(2 + -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 '(1 + -1v)' equal to zero and attempt to solve:

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

Simplifying
v = 1

Subproblem 3
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
Solution
v = {0, 1, 2}

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