5v^2+45v+90=0

Solution for 5v^2+45v+90=0 equation:

Simplifying
5v2 + 45v + 90 = 0

Reorder the terms:
90 + 45v + 5v2 = 0

Solving
90 + 45v + 5v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '5'.
5(18 + 9v + v2) = 0

Factor a trinomial.
5((6 + v)(3 + v)) = 0

Ignore the factor 5.
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 '(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 = {-6, -3}