3q^2+16q-12=0

Solution for 3q^2+16q-12=0 equation:

Simplifying
3q2 + 16q + -12 = 0

Reorder the terms:
-12 + 16q + 3q2 = 0

Solving
-12 + 16q + 3q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-6 + -1q)(2 + -3q) = 0

Subproblem 1
Set the factor '(-6 + -1q)' equal to zero and attempt to solve:

Simplifying
-6 + -1q = 0

Solving
-6 + -1q = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1q = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1q = 0 + 6
-1q = 0 + 6

Combine like terms: 0 + 6 = 6
-1q = 6

Divide each side by '-1'.
q = -6

Simplifying
q = -6
Subproblem 2
Set the factor '(2 + -3q)' equal to zero and attempt to solve:

Simplifying
2 + -3q = 0

Solving
2 + -3q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3q = 0 + -2
-3q = 0 + -2

Combine like terms: 0 + -2 = -2
-3q = -2

Divide each side by '-3'.
q = 0.6666666667

Simplifying
q = 0.6666666667
Solution
q = {-6, 0.6666666667}