2q+4q^2+6(1-q^1-q^2)=

Solution for 2q+4q^2+6(1-q^1-q^2)= equation:

Simplifying
2q + 4q2 + 6(1 + -1q + -1q2) = 0
2q + 4q2 + (1 * 6 + -1q * 6 + -1q2 * 6) = 0
2q + 4q2 + (6 + -6q + -6q2) = 0

Reorder the terms:
6 + 2q + -6q + 4q2 + -6q2 = 0

Combine like terms: 2q + -6q = -4q
6 + -4q + 4q2 + -6q2 = 0

Combine like terms: 4q2 + -6q2 = -2q2
6 + -4q + -2q2 = 0

Solving
6 + -4q + -2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2q + -1q2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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 = {1, -3}