6=q+q^2

Solution for 6=q+q^2 equation:

Simplifying
6 = q + q2

Solving
6 = q + q2

Solving for variable 'q'.

Reorder the terms:
6 + -1q + -1q2 = q + -1q + q2 + -1q2

Combine like terms: q + -1q = 0
6 + -1q + -1q2 = 0 + q2 + -1q2
6 + -1q + -1q2 = q2 + -1q2

Combine like terms: q2 + -1q2 = 0
6 + -1q + -1q2 = 0

Factor a trinomial.
(2 + -1q)(3 + q) = 0

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

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

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

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

Divide each side by '-1'.
q = 2

Simplifying
q = 2
Subproblem 2
Set the factor '(3 + q)' equal to zero and attempt to solve:

Simplifying
3 + q = 0

Solving
3 + q = 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 + q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + q = 0 + -3
q = 0 + -3

Combine like terms: 0 + -3 = -3
q = -3

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