3q^2-8q-3=0

Solution for 3q^2-8q-3=0 equation:

Simplifying
3q2 + -8q + -3 = 0

Reorder the terms:
-3 + -8q + 3q2 = 0

Solving
-3 + -8q + 3q2 = 0

Solving for variable 'q'.

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

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

Simplifying
-1 + -3q = 0

Solving
-1 + -3q = 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 + -3q = 0 + 1

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

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

Divide each side by '-3'.
q = -0.3333333333

Simplifying
q = -0.3333333333
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 = {-0.3333333333, 3}