10v^2+72v+72=0

Solution for 10v^2+72v+72=0 equation:

Simplifying
10v2 + 72v + 72 = 0

Reorder the terms:
72 + 72v + 10v2 = 0

Solving
72 + 72v + 10v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + 36v + 5v2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Subproblem 2
Set the factor '(6 + 5v)' equal to zero and attempt to solve:

Simplifying
6 + 5v = 0

Solving
6 + 5v = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5v = 0 + -6
5v = 0 + -6

Combine like terms: 0 + -6 = -6
5v = -6

Divide each side by '5'.
v = -1.2

Simplifying
v = -1.2
Solution
v = {-6, -1.2}