v^2=6+5v

Solution for v^2=6+5v equation:

Simplifying
v2 = 6 + 5v

Solving
v2 = 6 + 5v

Solving for variable 'v'.

Reorder the terms:
-6 + -5v + v2 = 6 + 5v + -6 + -5v

Reorder the terms:
-6 + -5v + v2 = 6 + -6 + 5v + -5v

Combine like terms: 6 + -6 = 0
-6 + -5v + v2 = 0 + 5v + -5v
-6 + -5v + v2 = 5v + -5v

Combine like terms: 5v + -5v = 0
-6 + -5v + v2 = 0

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

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

Simplifying
-1 + -1v = 0

Solving
-1 + -1v = 0

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

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

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

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

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

Simplifying
v = -1
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 = {-1, 6}