(3q^2-7q-6)=0

Solution for (3q^2-7q-6)=0 equation:

Simplifying
(3q2 + -7q + -6) = 0

Reorder the terms:
(-6 + -7q + 3q2) = 0

Remove parenthesis around (-6 + -7q + 3q2)
-6 + -7q + 3q2 = 0

Solving
-6 + -7q + 3q2 = 0

Solving for variable 'q'.

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

Subproblem 1
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
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 = {-0.6666666667, 3}