8v^2+4v-8=4v^2

Solution for 8v^2+4v-8=4v^2 equation:

Simplifying
8v2 + 4v + -8 = 4v2

Reorder the terms:
-8 + 4v + 8v2 = 4v2

Solving
-8 + 4v + 8v2 = 4v2

Solving for variable 'v'.

Combine like terms: 8v2 + -4v2 = 4v2
-8 + 4v + 4v2 = 4v2 + -4v2

Combine like terms: 4v2 + -4v2 = 0
-8 + 4v + 4v2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + v + v2) = 0

Factor a trinomial.
4((-2 + -1v)(1 + -1v)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
v = {-2, 1}