-v^2=36-12v

Solution for -v^2=36-12v equation:

Simplifying
-1v2 = 36 + -12v

Solving
-1v2 = 36 + -12v

Solving for variable 'v'.

Reorder the terms:
-36 + 12v + -1v2 = 36 + -12v + -36 + 12v

Reorder the terms:
-36 + 12v + -1v2 = 36 + -36 + -12v + 12v

Combine like terms: 36 + -36 = 0
-36 + 12v + -1v2 = 0 + -12v + 12v
-36 + 12v + -1v2 = -12v + 12v

Combine like terms: -12v + 12v = 0
-36 + 12v + -1v2 = 0

Factor a trinomial.
(-6 + v)(6 + -1v) = 0

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 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 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 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

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