2q^2-22q+48=0

Solution for 2q^2-22q+48=0 equation:

Simplifying
2q2 + -22q + 48 = 0

Reorder the terms:
48 + -22q + 2q2 = 0

Solving
48 + -22q + 2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -11q + q2) = 0

Factor a trinomial.
2((3 + -1q)(8 + -1q)) = 0

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

Simplifying
3 + -1q = 0

Solving
3 + -1q = 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 + -1q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1q = 0 + -3
-1q = 0 + -3

Combine like terms: 0 + -3 = -3
-1q = -3

Divide each side by '-1'.
q = 3

Simplifying
q = 3
Subproblem 2
Set the factor '(8 + -1q)' equal to zero and attempt to solve:

Simplifying
8 + -1q = 0

Solving
8 + -1q = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1q = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1q = 0 + -8
-1q = 0 + -8

Combine like terms: 0 + -8 = -8
-1q = -8

Divide each side by '-1'.
q = 8

Simplifying
q = 8
Solution
q = {3, 8}