5q^2-12q-9=0

Solution for 5q^2-12q-9=0 equation:

Simplifying
5q2 + -12q + -9 = 0

Reorder the terms:
-9 + -12q + 5q2 = 0

Solving
-9 + -12q + 5q2 = 0

Solving for variable 'q'.

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

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

Simplifying
-3 + -5q = 0

Solving
-3 + -5q = 0

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

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

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

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

Divide each side by '-5'.
q = -0.6

Simplifying
q = -0.6
Subproblem 2
Set the factor '(3 + -1q)' equal to zero and attempt to solve:

Simplifying
3 + -1q = 0

Solving
3 + -1q = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1q = 0 + -3
-1q = 0 + -3

Combine like terms: 0 + -3 = -3
-1q = -3

Divide each side by '-1'.
q = 3

Simplifying
q = 3
Solution
q = {-0.6, 3}