8q^2-10q+3=0

Solution for 8q^2-10q+3=0 equation:

Simplifying
8q2 + -10q + 3 = 0

Reorder the terms:
3 + -10q + 8q2 = 0

Solving
3 + -10q + 8q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(1 + -2q)(3 + -4q) = 0

Subproblem 1
Set the factor '(1 + -2q)' equal to zero and attempt to solve:

Simplifying
1 + -2q = 0

Solving
1 + -2q = 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 + -2q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2q = 0 + -1
-2q = 0 + -1

Combine like terms: 0 + -1 = -1
-2q = -1

Divide each side by '-2'.
q = 0.5

Simplifying
q = 0.5
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 = {0.5, 0.75}