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

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

Simplifying
(2q + 1)(q + 1) = 2(1 + -1q) + 6

Reorder the terms:
(1 + 2q)(q + 1) = 2(1 + -1q) + 6

Reorder the terms:
(1 + 2q)(1 + q) = 2(1 + -1q) + 6

Multiply (1 + 2q) * (1 + q)
(1(1 + q) + 2q * (1 + q)) = 2(1 + -1q) + 6
((1 * 1 + q * 1) + 2q * (1 + q)) = 2(1 + -1q) + 6
((1 + 1q) + 2q * (1 + q)) = 2(1 + -1q) + 6
(1 + 1q + (1 * 2q + q * 2q)) = 2(1 + -1q) + 6
(1 + 1q + (2q + 2q2)) = 2(1 + -1q) + 6

Combine like terms: 1q + 2q = 3q
(1 + 3q + 2q2) = 2(1 + -1q) + 6
1 + 3q + 2q2 = (1 * 2 + -1q * 2) + 6
1 + 3q + 2q2 = (2 + -2q) + 6

Reorder the terms:
1 + 3q + 2q2 = 2 + 6 + -2q

Combine like terms: 2 + 6 = 8
1 + 3q + 2q2 = 8 + -2q

Solving
1 + 3q + 2q2 = 8 + -2q

Solving for variable 'q'.

Reorder the terms:
1 + -8 + 3q + 2q + 2q2 = 8 + -2q + -8 + 2q

Combine like terms: 1 + -8 = -7
-7 + 3q + 2q + 2q2 = 8 + -2q + -8 + 2q

Combine like terms: 3q + 2q = 5q
-7 + 5q + 2q2 = 8 + -2q + -8 + 2q

Reorder the terms:
-7 + 5q + 2q2 = 8 + -8 + -2q + 2q

Combine like terms: 8 + -8 = 0
-7 + 5q + 2q2 = 0 + -2q + 2q
-7 + 5q + 2q2 = -2q + 2q

Combine like terms: -2q + 2q = 0
-7 + 5q + 2q2 = 0

Factor a trinomial.
(-7 + -2q)(1 + -1q) = 0

Subproblem 1
Set the factor '(-7 + -2q)' equal to zero and attempt to solve:

Simplifying
-7 + -2q = 0

Solving
-7 + -2q = 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 + -2q = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2q = 0 + 7
-2q = 0 + 7

Combine like terms: 0 + 7 = 7
-2q = 7

Divide each side by '-2'.
q = -3.5

Simplifying
q = -3.5
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 = {-3.5, 1}