8v^2-23v-124=-4-7v

Solution for 8v^2-23v-124=-4-7v equation:

Simplifying
8v2 + -23v + -124 = -4 + -7v

Reorder the terms:
-124 + -23v + 8v2 = -4 + -7v

Solving
-124 + -23v + 8v2 = -4 + -7v

Solving for variable 'v'.

Reorder the terms:
-124 + 4 + -23v + 7v + 8v2 = -4 + -7v + 4 + 7v

Combine like terms: -124 + 4 = -120
-120 + -23v + 7v + 8v2 = -4 + -7v + 4 + 7v

Combine like terms: -23v + 7v = -16v
-120 + -16v + 8v2 = -4 + -7v + 4 + 7v

Reorder the terms:
-120 + -16v + 8v2 = -4 + 4 + -7v + 7v

Combine like terms: -4 + 4 = 0
-120 + -16v + 8v2 = 0 + -7v + 7v
-120 + -16v + 8v2 = -7v + 7v

Combine like terms: -7v + 7v = 0
-120 + -16v + 8v2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-15 + -2v + v2) = 0

Factor a trinomial.
8((-3 + -1v)(5 + -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 '(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
Solution
v = {-3, 5}