6(v-5)(v+2)=0

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Solution for 6(v-5)(v+2)=0 equation: 


Simplifying
6(v + -5)(v + 2) = 0

Reorder the terms:
6(-5 + v)(v + 2) = 0

Reorder the terms:
6(-5 + v)(2 + v) = 0

Multiply (-5 + v) * (2 + v)
6(-5(2 + v) + v(2 + v)) = 0
6((2 * -5 + v * -5) + v(2 + v)) = 0
6((-10 + -5v) + v(2 + v)) = 0
6(-10 + -5v + (2 * v + v * v)) = 0
6(-10 + -5v + (2v + v2)) = 0

Combine like terms: -5v + 2v = -3v
6(-10 + -3v + v2) = 0
(-10 * 6 + -3v * 6 + v2 * 6) = 0
(-60 + -18v + 6v2) = 0

Solving
-60 + -18v + 6v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-10 + -3v + v2) = 0

Factor a trinomial.
6((-2 + -1v)(5 + -1v)) = 0

Ignore the factor 6.

Subproblem 1
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 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
Solution
v = {-2, 5}

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