5q+3q^2+2(1-q^1-q^2)=

Solution for 5q+3q^2+2(1-q^1-q^2)= equation:

Simplifying
5q + 3q2 + 2(1 + -1q + -1q2) = 0
5q + 3q2 + (1 * 2 + -1q * 2 + -1q2 * 2) = 0
5q + 3q2 + (2 + -2q + -2q2) = 0

Reorder the terms:
2 + 5q + -2q + 3q2 + -2q2 = 0

Combine like terms: 5q + -2q = 3q
2 + 3q + 3q2 + -2q2 = 0

Combine like terms: 3q2 + -2q2 = 1q2
2 + 3q + 1q2 = 0

Solving
2 + 3q + 1q2 = 0

Solving for variable 'q'.

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

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

Simplifying
2 + q = 0

Solving
2 + q = 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 + q = 0 + -2

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

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

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

Simplifying
1 + q = 0

Solving
1 + q = 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 + q = 0 + -1

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

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

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