8v^2=-8v+48

Solution for 8v^2=-8v+48 equation:

Simplifying
8v2 = -8v + 48

Reorder the terms:
8v2 = 48 + -8v

Solving
8v2 = 48 + -8v

Solving for variable 'v'.

Reorder the terms:
-48 + 8v + 8v2 = 48 + -8v + -48 + 8v

Reorder the terms:
-48 + 8v + 8v2 = 48 + -48 + -8v + 8v

Combine like terms: 48 + -48 = 0
-48 + 8v + 8v2 = 0 + -8v + 8v
-48 + 8v + 8v2 = -8v + 8v

Combine like terms: -8v + 8v = 0
-48 + 8v + 8v2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + v + v2) = 0

Factor a trinomial.
8((-3 + -1v)(2 + -1v)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve:

Simplifying
-3 + -1v = 0

Solving
-3 + -1v = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1v = 0 + 3
-1v = 0 + 3

Combine like terms: 0 + 3 = 3
-1v = 3

Divide each side by '-1'.
v = -3

Simplifying
v = -3
Subproblem 2
Set the factor '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2
Solution
v = {-3, 2}