2q^2-44q-46=0

Solution for 2q^2-44q-46=0 equation:

Simplifying
2q2 + -44q + -46 = 0

Reorder the terms:
-46 + -44q + 2q2 = 0

Solving
-46 + -44q + 2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-23 + -22q + q2) = 0

Factor a trinomial.
2((-1 + -1q)(23 + -1q)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(23 + -1q)' equal to zero and attempt to solve:

Simplifying
23 + -1q = 0

Solving
23 + -1q = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1q = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1q = 0 + -23
-1q = 0 + -23

Combine like terms: 0 + -23 = -23
-1q = -23

Divide each side by '-1'.
q = 23

Simplifying
q = 23
Solution
q = {-1, 23}