5q^2-8q+3=0

Solution for 5q^2-8q+3=0 equation:

Simplifying
5q2 + -8q + 3 = 0

Reorder the terms:
3 + -8q + 5q2 = 0

Solving
3 + -8q + 5q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(3 + -5q)(1 + -1q) = 0

Subproblem 1
Set the factor '(3 + -5q)' equal to zero and attempt to solve:

Simplifying
3 + -5q = 0

Solving
3 + -5q = 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 + -5q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5q = 0 + -3
-5q = 0 + -3

Combine like terms: 0 + -3 = -3
-5q = -3

Divide each side by '-5'.
q = 0.6

Simplifying
q = 0.6
Subproblem 2
Set the factor '(1 + -1q)' equal to zero and attempt to solve:

Simplifying
1 + -1q = 0

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

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

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

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

Simplifying
q = 1
Solution
q = {0.6, 1}