v^2=30-v

Solution for v^2=30-v equation:

Simplifying
v2 = 30 + -1v

Solving
v2 = 30 + -1v

Solving for variable 'v'.

Reorder the terms:
-30 + v + v2 = 30 + -1v + -30 + v

Reorder the terms:
-30 + v + v2 = 30 + -30 + -1v + v

Combine like terms: 30 + -30 = 0
-30 + v + v2 = 0 + -1v + v
-30 + v + v2 = -1v + v

Combine like terms: -1v + v = 0
-30 + v + v2 = 0

Factor a trinomial.
(-6 + -1v)(5 + -1v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {-6, 5}