5v^2-9v=72

Solution for 5v^2-9v=72 equation:

Simplifying
5v2 + -9v = 72

Reorder the terms:
-9v + 5v2 = 72

Solving
-9v + 5v2 = 72

Solving for variable 'v'.

Reorder the terms:
-72 + -9v + 5v2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -9v + 5v2 = 0

Factor a trinomial.
(-3 + -1v)(24 + -5v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(24 + -5v)' equal to zero and attempt to solve:

Simplifying
24 + -5v = 0

Solving
24 + -5v = 0

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

Add '-24' to each side of the equation.
24 + -24 + -5v = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -5v = 0 + -24
-5v = 0 + -24

Combine like terms: 0 + -24 = -24
-5v = -24

Divide each side by '-5'.
v = 4.8

Simplifying
v = 4.8
Solution
v = {-3, 4.8}