-9v(v+3)+4v+6=8v+6

Solution for -9v(v+3)+4v+6=8v+6 equation:

Simplifying
-9v(v + 3) + 4v + 6 = 8v + 6

Reorder the terms:
-9v(3 + v) + 4v + 6 = 8v + 6
(3 * -9v + v * -9v) + 4v + 6 = 8v + 6
(-27v + -9v2) + 4v + 6 = 8v + 6

Reorder the terms:
6 + -27v + 4v + -9v2 = 8v + 6

Combine like terms: -27v + 4v = -23v
6 + -23v + -9v2 = 8v + 6

Reorder the terms:
6 + -23v + -9v2 = 6 + 8v

Add '-6' to each side of the equation.
6 + -23v + -6 + -9v2 = 6 + -6 + 8v

Reorder the terms:
6 + -6 + -23v + -9v2 = 6 + -6 + 8v

Combine like terms: 6 + -6 = 0
0 + -23v + -9v2 = 6 + -6 + 8v
-23v + -9v2 = 6 + -6 + 8v

Combine like terms: 6 + -6 = 0
-23v + -9v2 = 0 + 8v
-23v + -9v2 = 8v

Solving
-23v + -9v2 = 8v

Solving for variable 'v'.

Reorder the terms:
-23v + -8v + -9v2 = 8v + -8v

Combine like terms: -23v + -8v = -31v
-31v + -9v2 = 8v + -8v

Combine like terms: 8v + -8v = 0
-31v + -9v2 = 0

Factor out the Greatest Common Factor (GCF), '-1v'.
-1v(31 + 9v) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'v' equal to zero and attempt to solve:

Simplifying
v = 0

Solving
v = 0

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

Simplifying
v = 0
Subproblem 2
Set the factor '(31 + 9v)' equal to zero and attempt to solve:

Simplifying
31 + 9v = 0

Solving
31 + 9v = 0

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

Add '-31' to each side of the equation.
31 + -31 + 9v = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 9v = 0 + -31
9v = 0 + -31

Combine like terms: 0 + -31 = -31
9v = -31

Divide each side by '9'.
v = -3.444444444

Simplifying
v = -3.444444444
Solution
v = {0, -3.444444444}