12q^2-17q-5=0

Solution for 12q^2-17q-5=0 equation:

Simplifying
12q2 + -17q + -5 = 0

Reorder the terms:
-5 + -17q + 12q2 = 0

Solving
-5 + -17q + 12q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-1 + -4q)(5 + -3q) = 0

Subproblem 1
Set the factor '(-1 + -4q)' equal to zero and attempt to solve:

Simplifying
-1 + -4q = 0

Solving
-1 + -4q = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4q = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4q = 0 + 1
-4q = 0 + 1

Combine like terms: 0 + 1 = 1
-4q = 1

Divide each side by '-4'.
q = -0.25

Simplifying
q = -0.25
Subproblem 2
Set the factor '(5 + -3q)' equal to zero and attempt to solve:

Simplifying
5 + -3q = 0

Solving
5 + -3q = 0

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

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

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

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

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

Simplifying
q = 1.666666667
Solution
q = {-0.25, 1.666666667}