16q^2-8q-3=0

Solution for 16q^2-8q-3=0 equation:

Simplifying
16q2 + -8q + -3 = 0

Reorder the terms:
-3 + -8q + 16q2 = 0

Solving
-3 + -8q + 16q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-1 + -4q)(3 + -4q) = 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 '(3 + -4q)' equal to zero and attempt to solve:

Simplifying
3 + -4q = 0

Solving
3 + -4q = 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 + -4q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4q = 0 + -3
-4q = 0 + -3

Combine like terms: 0 + -3 = -3
-4q = -3

Divide each side by '-4'.
q = 0.75

Simplifying
q = 0.75
Solution
q = {-0.25, 0.75}