374=-q^2-2q+517

Solution for 374=-q^2-2q+517 equation:

Simplifying
374 = -1q2 + -2q + 517

Reorder the terms:
374 = 517 + -2q + -1q2

Solving
374 = 517 + -2q + -1q2

Solving for variable 'q'.

Combine like terms: 374 + -517 = -143
-143 + 2q + q2 = 517 + -2q + -1q2 + -517 + 2q + q2

Reorder the terms:
-143 + 2q + q2 = 517 + -517 + -2q + 2q + -1q2 + q2

Combine like terms: 517 + -517 = 0
-143 + 2q + q2 = 0 + -2q + 2q + -1q2 + q2
-143 + 2q + q2 = -2q + 2q + -1q2 + q2

Combine like terms: -2q + 2q = 0
-143 + 2q + q2 = 0 + -1q2 + q2
-143 + 2q + q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
-143 + 2q + q2 = 0

Factor a trinomial.
(-13 + -1q)(11 + -1q) = 0

Subproblem 1
Set the factor '(-13 + -1q)' equal to zero and attempt to solve:

Simplifying
-13 + -1q = 0

Solving
-13 + -1q = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1q = 0 + 13

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

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

Divide each side by '-1'.
q = -13

Simplifying
q = -13
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 = {-13, 11}