6v^2+17v-45=0

Solution for 6v^2+17v-45=0 equation:

Simplifying
6v2 + 17v + -45 = 0

Reorder the terms:
-45 + 17v + 6v2 = 0

Solving
-45 + 17v + 6v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-9 + -2v)(5 + -3v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -3v)' equal to zero and attempt to solve:

Simplifying
5 + -3v = 0

Solving
5 + -3v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3v = 0 + -5
-3v = 0 + -5

Combine like terms: 0 + -5 = -5
-3v = -5

Divide each side by '-3'.
v = 1.666666667

Simplifying
v = 1.666666667
Solution
v = {-4.5, 1.666666667}