8q^2-40q+42=0

Solution for 8q^2-40q+42=0 equation:

Simplifying
8q2 + -40q + 42 = 0

Reorder the terms:
42 + -40q + 8q2 = 0

Solving
42 + -40q + 8q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -20q + 4q2) = 0

Factor a trinomial.
2((3 + -2q)(7 + -2q)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -2q)' equal to zero and attempt to solve:

Simplifying
3 + -2q = 0

Solving
3 + -2q = 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 + -2q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2q = 0 + -3
-2q = 0 + -3

Combine like terms: 0 + -3 = -3
-2q = -3

Divide each side by '-2'.
q = 1.5

Simplifying
q = 1.5
Subproblem 2
Set the factor '(7 + -2q)' equal to zero and attempt to solve:

Simplifying
7 + -2q = 0

Solving
7 + -2q = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2q = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2q = 0 + -7
-2q = 0 + -7

Combine like terms: 0 + -7 = -7
-2q = -7

Divide each side by '-2'.
q = 3.5

Simplifying
q = 3.5
Solution
q = {1.5, 3.5}