60q^2-130q+50=0

Solution for 60q^2-130q+50=0 equation:

Simplifying
60q2 + -130q + 50 = 0

Reorder the terms:
50 + -130q + 60q2 = 0

Solving
50 + -130q + 60q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '10'.
10(5 + -13q + 6q2) = 0

Factor a trinomial.
10((1 + -2q)(5 + -3q)) = 0

Ignore the factor 10.
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 '(5 + -3q)' equal to zero and attempt to solve:

Simplifying
5 + -3q = 0

Solving
5 + -3q = 0

Move all terms containing q to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -3q = 0 + -5

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

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

Divide each side by '-3'.
q = 1.666666667

Simplifying
q = 1.666666667
Solution
q = {0.5, 1.666666667}