v^2=-54-15v

Solution for v^2=-54-15v equation:

Simplifying
v2 = -54 + -15v

Solving
v2 = -54 + -15v

Solving for variable 'v'.

Reorder the terms:
54 + 15v + v2 = -54 + -15v + 54 + 15v

Reorder the terms:
54 + 15v + v2 = -54 + 54 + -15v + 15v

Combine like terms: -54 + 54 = 0
54 + 15v + v2 = 0 + -15v + 15v
54 + 15v + v2 = -15v + 15v

Combine like terms: -15v + 15v = 0
54 + 15v + v2 = 0

Factor a trinomial.
(9 + v)(6 + v) = 0

Subproblem 1
Set the factor '(9 + v)' equal to zero and attempt to solve:

Simplifying
9 + v = 0

Solving
9 + v = 0

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

Add '-9' to each side of the equation.
9 + -9 + v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + v = 0 + -9
v = 0 + -9

Combine like terms: 0 + -9 = -9
v = -9

Simplifying
v = -9
Subproblem 2
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
Solution
v = {-9, -6}