v^2=v+30

Solution for v^2=v+30 equation:

Simplifying
v2 = v + 30

Reorder the terms:
v2 = 30 + v

Solving
v2 = 30 + v

Solving for variable 'v'.

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

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

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

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

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

Subproblem 1
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
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 = {-5, 6}