q^2-8q=33

Solution for q^2-8q=33 equation:

Simplifying
q2 + -8q = 33

Reorder the terms:
-8q + q2 = 33

Solving
-8q + q2 = 33

Solving for variable 'q'.

Reorder the terms:
-33 + -8q + q2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + -8q + q2 = 0

Factor a trinomial.
(-3 + -1q)(11 + -1q) = 0

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 '(11 + -1q)' equal to zero and attempt to solve:

Simplifying
11 + -1q = 0

Solving
11 + -1q = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1q = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1q = 0 + -11
-1q = 0 + -11

Combine like terms: 0 + -11 = -11
-1q = -11

Divide each side by '-1'.
q = 11

Simplifying
q = 11
Solution
q = {-3, 11}