6q-(q-2)=3q+2q(q+1)

Solution for 6q-(q-2)=3q+2q(q+1) equation:

Simplifying
6q + -1(q + -2) = 3q + 2q(q + 1)

Reorder the terms:
6q + -1(-2 + q) = 3q + 2q(q + 1)
6q + (-2 * -1 + q * -1) = 3q + 2q(q + 1)
6q + (2 + -1q) = 3q + 2q(q + 1)

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

Combine like terms: 6q + -1q = 5q
2 + 5q = 3q + 2q(q + 1)

Reorder the terms:
2 + 5q = 3q + 2q(1 + q)
2 + 5q = 3q + (1 * 2q + q * 2q)
2 + 5q = 3q + (2q + 2q2)

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

Add '-5q' to each side of the equation.
2 + 5q + -5q = 5q + -5q + 2q2

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

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

Solving
2 = 2q2

Solving for variable 'q'.

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

Add '-2q2' to each side of the equation.
2 + -2q2 = 2q2 + -2q2

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

Add '-2' to each side of the equation.
2 + -2 + -2q2 = 0 + -2

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

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

Divide each side by '-2'.
q2 = 1

Simplifying
q2 = 1

Take the square root of each side:
q = {-1, 1}