9q-q(q-2)=6q+2(q+1)

Solution for 9q-q(q-2)=6q+2(q+1) equation:

Simplifying
9q + -1q(q + -2) = 6q + 2(q + 1)

Reorder the terms:
9q + -1q(-2 + q) = 6q + 2(q + 1)
9q + (-2 * -1q + q * -1q) = 6q + 2(q + 1)
9q + (2q + -1q2) = 6q + 2(q + 1)

Combine like terms: 9q + 2q = 11q
11q + -1q2 = 6q + 2(q + 1)

Reorder the terms:
11q + -1q2 = 6q + 2(1 + q)
11q + -1q2 = 6q + (1 * 2 + q * 2)
11q + -1q2 = 6q + (2 + 2q)

Reorder the terms:
11q + -1q2 = 2 + 6q + 2q

Combine like terms: 6q + 2q = 8q
11q + -1q2 = 2 + 8q

Solving
11q + -1q2 = 2 + 8q

Solving for variable 'q'.

Reorder the terms:
-2 + 11q + -8q + -1q2 = 2 + 8q + -2 + -8q

Combine like terms: 11q + -8q = 3q
-2 + 3q + -1q2 = 2 + 8q + -2 + -8q

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

Combine like terms: 2 + -2 = 0
-2 + 3q + -1q2 = 0 + 8q + -8q
-2 + 3q + -1q2 = 8q + -8q

Combine like terms: 8q + -8q = 0
-2 + 3q + -1q2 = 0

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