6v^2-18v=60

Solution for 6v^2-18v=60 equation:

Simplifying
6v2 + -18v = 60

Reorder the terms:
-18v + 6v2 = 60

Solving
-18v + 6v2 = 60

Solving for variable 'v'.

Reorder the terms:
-60 + -18v + 6v2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -18v + 6v2 = 0

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}