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

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

Simplifying
q2 = 2(q + -1)(q + 2)

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

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

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

Combine like terms: -1q + 2q = 1q
q2 = 2(-2 + 1q + q2)
q2 = (-2 * 2 + 1q * 2 + q2 * 2)
q2 = (-4 + 2q + 2q2)

Solving
q2 = -4 + 2q + 2q2

Solving for variable 'q'.

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

Combine like terms: q2 + -2q2 = -1q2
4 + -2q + -1q2 = -4 + 2q + 2q2 + 4 + -2q + -2q2

Reorder the terms:
4 + -2q + -1q2 = -4 + 4 + 2q + -2q + 2q2 + -2q2

Combine like terms: -4 + 4 = 0
4 + -2q + -1q2 = 0 + 2q + -2q + 2q2 + -2q2
4 + -2q + -1q2 = 2q + -2q + 2q2 + -2q2

Combine like terms: 2q + -2q = 0
4 + -2q + -1q2 = 0 + 2q2 + -2q2
4 + -2q + -1q2 = 2q2 + -2q2

Combine like terms: 2q2 + -2q2 = 0
4 + -2q + -1q2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 2q + q2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2q + 4 + q2 = 0 + 4

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

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

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

The q term is 2q.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2q + 1 + q2 = 4 + 1

Reorder the terms:
1 + 2q + q2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + 2q + q2 = 5

Factor a perfect square on the left side:
(q + 1)(q + 1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(q + 1) equal to 2.236067978 and -2.236067978.

Subproblem 1
q + 1 = 2.236067978

Simplifying
q + 1 = 2.236067978

Reorder the terms:
1 + q = 2.236067978

Solving
1 + q = 2.236067978

Solving for variable 'q'.

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 = 2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + q = 2.236067978 + -1
q = 2.236067978 + -1

Combine like terms: 2.236067978 + -1 = 1.236067978
q = 1.236067978

Simplifying
q = 1.236067978

Subproblem 2
q + 1 = -2.236067978

Simplifying
q + 1 = -2.236067978

Reorder the terms:
1 + q = -2.236067978

Solving
1 + q = -2.236067978

Solving for variable 'q'.

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 = -2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + q = -2.236067978 + -1
q = -2.236067978 + -1

Combine like terms: -2.236067978 + -1 = -3.236067978
q = -3.236067978

Simplifying
q = -3.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {1.236067978, -3.236067978}