6v^2+78v+180=0

Solution for 6v^2+78v+180=0 equation:

Simplifying
6v2 + 78v + 180 = 0

Reorder the terms:
180 + 78v + 6v2 = 0

Solving
180 + 78v + 6v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '6'.
6(30 + 13v + v2) = 0

Factor a trinomial.
6((10 + v)(3 + v)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(10 + v)' equal to zero and attempt to solve:

Simplifying
10 + v = 0

Solving
10 + v = 0

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

Add '-10' to each side of the equation.
10 + -10 + v = 0 + -10

Combine like terms: 10 + -10 = 0
0 + v = 0 + -10
v = 0 + -10

Combine like terms: 0 + -10 = -10
v = -10

Simplifying
v = -10
Subproblem 2
Set the factor '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

Solving
3 + v = 0

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

Add '-3' to each side of the equation.
3 + -3 + v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + v = 0 + -3
v = 0 + -3

Combine like terms: 0 + -3 = -3
v = -3

Simplifying
v = -3
Solution
v = {-10, -3}