30v^2-81v+54=0

Solution for 30v^2-81v+54=0 equation:

Simplifying
30v2 + -81v + 54 = 0

Reorder the terms:
54 + -81v + 30v2 = 0

Solving
54 + -81v + 30v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -27v + 10v2) = 0

Factor a trinomial.
3((6 + -5v)(3 + -2v)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -5v)' equal to zero and attempt to solve:

Simplifying
6 + -5v = 0

Solving
6 + -5v = 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 + -5v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5v = 0 + -6
-5v = 0 + -6

Combine like terms: 0 + -6 = -6
-5v = -6

Divide each side by '-5'.
v = 1.2

Simplifying
v = 1.2
Subproblem 2
Set the factor '(3 + -2v)' equal to zero and attempt to solve:

Simplifying
3 + -2v = 0

Solving
3 + -2v = 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 + -2v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2v = 0 + -3
-2v = 0 + -3

Combine like terms: 0 + -3 = -3
-2v = -3

Divide each side by '-2'.
v = 1.5

Simplifying
v = 1.5
Solution
v = {1.2, 1.5}