42q^2-23q+1=0

Solution for 42q^2-23q+1=0 equation:

Simplifying
42q2 + -23q + 1 = 0

Reorder the terms:
1 + -23q + 42q2 = 0

Solving
1 + -23q + 42q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(1 + -21q)(1 + -2q) = 0

Subproblem 1
Set the factor '(1 + -21q)' equal to zero and attempt to solve:

Simplifying
1 + -21q = 0

Solving
1 + -21q = 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 + -21q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -21q = 0 + -1
-21q = 0 + -1

Combine like terms: 0 + -1 = -1
-21q = -1

Divide each side by '-21'.
q = 0.04761904762

Simplifying
q = 0.04761904762
Subproblem 2
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
Solution
q = {0.04761904762, 0.5}