42q^2-259q+42=0

Solution for 42q^2-259q+42=0 equation:

Simplifying
42q2 + -259q + 42 = 0

Reorder the terms:
42 + -259q + 42q2 = 0

Solving
42 + -259q + 42q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '7'.
7(6 + -37q + 6q2) = 0

Factor a trinomial.
7((1 + -6q)(6 + -1q)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(1 + -6q)' equal to zero and attempt to solve:

Simplifying
1 + -6q = 0

Solving
1 + -6q = 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 + -6q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6q = 0 + -1
-6q = 0 + -1

Combine like terms: 0 + -1 = -1
-6q = -1

Divide each side by '-6'.
q = 0.1666666667

Simplifying
q = 0.1666666667
Subproblem 2
Set the factor '(6 + -1q)' equal to zero and attempt to solve:

Simplifying
6 + -1q = 0

Solving
6 + -1q = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1q = 0 + -6
-1q = 0 + -6

Combine like terms: 0 + -6 = -6
-1q = -6

Divide each side by '-1'.
q = 6

Simplifying
q = 6
Solution
q = {0.1666666667, 6}