10v^2-57v+54=0

Solution for 10v^2-57v+54=0 equation:

Simplifying
10v2 + -57v + 54 = 0

Reorder the terms:
54 + -57v + 10v2 = 0

Solving
54 + -57v + 10v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + -5v)(9 + -2v) = 0

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 '(9 + -2v)' equal to zero and attempt to solve:

Simplifying
9 + -2v = 0

Solving
9 + -2v = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2v = 0 + -9
-2v = 0 + -9

Combine like terms: 0 + -9 = -9
-2v = -9

Divide each side by '-2'.
v = 4.5

Simplifying
v = 4.5
Solution
v = {1.2, 4.5}