3v^2+9v=54

Solution for 3v^2+9v=54 equation:

Simplifying
3v2 + 9v = 54

Reorder the terms:
9v + 3v2 = 54

Solving
9v + 3v2 = 54

Solving for variable 'v'.

Reorder the terms:
-54 + 9v + 3v2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 9v + 3v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + 3v + v2) = 0

Factor a trinomial.
3((-6 + -1v)(3 + -1v)) = 0

Ignore the factor 3.
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 '(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
Solution
v = {-6, 3}