-21=-q^2-4q

Solution for -21=-q^2-4q equation:

Simplifying
-21 = -1q2 + -4q

Reorder the terms:
-21 = -4q + -1q2

Solving
-21 = -4q + -1q2

Solving for variable 'q'.

Reorder the terms:
-21 + 4q + q2 = -4q + 4q + -1q2 + q2

Combine like terms: -4q + 4q = 0
-21 + 4q + q2 = 0 + -1q2 + q2
-21 + 4q + q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
-21 + 4q + q2 = 0

Factor a trinomial.
(-7 + -1q)(3 + -1q) = 0

Subproblem 1
Set the factor '(-7 + -1q)' equal to zero and attempt to solve:

Simplifying
-7 + -1q = 0

Solving
-7 + -1q = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1q = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1q = 0 + 7
-1q = 0 + 7

Combine like terms: 0 + 7 = 7
-1q = 7

Divide each side by '-1'.
q = -7

Simplifying
q = -7
Subproblem 2
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
Solution
q = {-7, 3}