12q^2+17q-40=0

Solution for 12q^2+17q-40=0 equation:

Simplifying
12q2 + 17q + -40 = 0

Reorder the terms:
-40 + 17q + 12q2 = 0

Solving
-40 + 17q + 12q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-8 + -3q)(5 + -4q) = 0

Subproblem 1
Set the factor '(-8 + -3q)' equal to zero and attempt to solve:

Simplifying
-8 + -3q = 0

Solving
-8 + -3q = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3q = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3q = 0 + 8
-3q = 0 + 8

Combine like terms: 0 + 8 = 8
-3q = 8

Divide each side by '-3'.
q = -2.666666667

Simplifying
q = -2.666666667
Subproblem 2
Set the factor '(5 + -4q)' equal to zero and attempt to solve:

Simplifying
5 + -4q = 0

Solving
5 + -4q = 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 + -4q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4q = 0 + -5
-4q = 0 + -5

Combine like terms: 0 + -5 = -5
-4q = -5

Divide each side by '-4'.
q = 1.25

Simplifying
q = 1.25
Solution
q = {-2.666666667, 1.25}