q^2-48q+351=0

Solution for q^2-48q+351=0 equation:

Simplifying
q2 + -48q + 351 = 0

Reorder the terms:
351 + -48q + q2 = 0

Solving
351 + -48q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(9 + -1q)(39 + -1q) = 0

Subproblem 1
Set the factor '(9 + -1q)' equal to zero and attempt to solve:

Simplifying
9 + -1q = 0

Solving
9 + -1q = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1q = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1q = 0 + -9
-1q = 0 + -9

Combine like terms: 0 + -9 = -9
-1q = -9

Divide each side by '-1'.
q = 9

Simplifying
q = 9
Subproblem 2
Set the factor '(39 + -1q)' equal to zero and attempt to solve:

Simplifying
39 + -1q = 0

Solving
39 + -1q = 0

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

Add '-39' to each side of the equation.
39 + -39 + -1q = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -1q = 0 + -39
-1q = 0 + -39

Combine like terms: 0 + -39 = -39
-1q = -39

Divide each side by '-1'.
q = 39

Simplifying
q = 39
Solution
q = {9, 39}