8v^2=240+8v

Solution for 8v^2=240+8v equation:

Simplifying
8v2 = 240 + 8v

Solving
8v2 = 240 + 8v

Solving for variable 'v'.

Reorder the terms:
-240 + -8v + 8v2 = 240 + 8v + -240 + -8v

Reorder the terms:
-240 + -8v + 8v2 = 240 + -240 + 8v + -8v

Combine like terms: 240 + -240 = 0
-240 + -8v + 8v2 = 0 + 8v + -8v
-240 + -8v + 8v2 = 8v + -8v

Combine like terms: 8v + -8v = 0
-240 + -8v + 8v2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-30 + -1v + v2) = 0

Factor a trinomial.
8((-5 + -1v)(6 + -1v)) = 0

Ignore the factor 8.
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}