54v^2+276v-288=0

Solution for 54v^2+276v-288=0 equation:

Simplifying
54v2 + 276v + -288 = 0

Reorder the terms:
-288 + 276v + 54v2 = 0

Solving
-288 + 276v + 54v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-48 + 46v + 9v2) = 0

Factor a trinomial.
6((-6 + -1v)(8 + -9v)) = 0

Ignore the factor 6.
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 '(8 + -9v)' equal to zero and attempt to solve:

Simplifying
8 + -9v = 0

Solving
8 + -9v = 0

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

Add '-8' to each side of the equation.
8 + -8 + -9v = 0 + -8

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

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

Divide each side by '-9'.
v = 0.8888888889

Simplifying
v = 0.8888888889
Solution
v = {-6, 0.8888888889}