533=q^2+13q+23

Solution for 533=q^2+13q+23 equation:

Simplifying
533 = q2 + 13q + 23

Reorder the terms:
533 = 23 + 13q + q2

Solving
533 = 23 + 13q + q2

Solving for variable 'q'.

Combine like terms: 533 + -23 = 510
510 + -13q + -1q2 = 23 + 13q + q2 + -23 + -13q + -1q2

Reorder the terms:
510 + -13q + -1q2 = 23 + -23 + 13q + -13q + q2 + -1q2

Combine like terms: 23 + -23 = 0
510 + -13q + -1q2 = 0 + 13q + -13q + q2 + -1q2
510 + -13q + -1q2 = 13q + -13q + q2 + -1q2

Combine like terms: 13q + -13q = 0
510 + -13q + -1q2 = 0 + q2 + -1q2
510 + -13q + -1q2 = q2 + -1q2

Combine like terms: q2 + -1q2 = 0
510 + -13q + -1q2 = 0

Factor a trinomial.
(17 + -1q)(30 + q) = 0

Subproblem 1
Set the factor '(17 + -1q)' equal to zero and attempt to solve:

Simplifying
17 + -1q = 0

Solving
17 + -1q = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1q = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1q = 0 + -17
-1q = 0 + -17

Combine like terms: 0 + -17 = -17
-1q = -17

Divide each side by '-1'.
q = 17

Simplifying
q = 17
Subproblem 2
Set the factor '(30 + q)' equal to zero and attempt to solve:

Simplifying
30 + q = 0

Solving
30 + q = 0

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

Add '-30' to each side of the equation.
30 + -30 + q = 0 + -30

Combine like terms: 30 + -30 = 0
0 + q = 0 + -30
q = 0 + -30

Combine like terms: 0 + -30 = -30
q = -30

Simplifying
q = -30
Solution
q = {17, -30}