(1+q+q^2)=3

Solution for (1+q+q^2)=3 equation:

Simplifying
(1 + q + q2) = 3

Remove parenthesis around (1 + q + q2)
1 + q + q2 = 3

Solving
1 + q + q2 = 3

Solving for variable 'q'.

Reorder the terms:
1 + -3 + q + q2 = 3 + -3

Combine like terms: 1 + -3 = -2
-2 + q + q2 = 3 + -3

Combine like terms: 3 + -3 = 0
-2 + q + q2 = 0

Factor a trinomial.
(-2 + -1q)(1 + -1q) = 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 '(1 + -1q)' equal to zero and attempt to solve:

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

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

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

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

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

Simplifying
q = 1
Solution
q = {-2, 1}