8v^2=336+8v

Solution for 8v^2=336+8v equation:

Simplifying
8v2 = 336 + 8v

Solving
8v2 = 336 + 8v

Solving for variable 'v'.

Reorder the terms:
-336 + -8v + 8v2 = 336 + 8v + -336 + -8v

Reorder the terms:
-336 + -8v + 8v2 = 336 + -336 + 8v + -8v

Combine like terms: 336 + -336 = 0
-336 + -8v + 8v2 = 0 + 8v + -8v
-336 + -8v + 8v2 = 8v + -8v

Combine like terms: 8v + -8v = 0
-336 + -8v + 8v2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-42 + -1v + v2) = 0

Factor a trinomial.
8((-6 + -1v)(7 + -1v)) = 0

Ignore the factor 8.
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 '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {-6, 7}