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

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

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

Reorder the terms:
2q(1 + 2q) = 3(q + -2)
(1 * 2q + 2q * 2q) = 3(q + -2)
(2q + 4q2) = 3(q + -2)

Reorder the terms:
2q + 4q2 = 3(-2 + q)
2q + 4q2 = (-2 * 3 + q * 3)
2q + 4q2 = (-6 + 3q)

Solving
2q + 4q2 = -6 + 3q

Solving for variable 'q'.

Reorder the terms:
6 + 2q + -3q + 4q2 = -6 + 3q + 6 + -3q

Combine like terms: 2q + -3q = -1q
6 + -1q + 4q2 = -6 + 3q + 6 + -3q

Reorder the terms:
6 + -1q + 4q2 = -6 + 6 + 3q + -3q

Combine like terms: -6 + 6 = 0
6 + -1q + 4q2 = 0 + 3q + -3q
6 + -1q + 4q2 = 3q + -3q

Combine like terms: 3q + -3q = 0
6 + -1q + 4q2 = 0

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

Divide each side by '4'.
1.5 + -0.25q + q2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.25q + -1.5 + q2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.25q + q2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.25q + q2 = 0 + -1.5
-0.25q + q2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.25q + q2 = -1.5

The q term is -0.25q.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25q + 0.015625 + q2 = -1.5 + 0.015625

Reorder the terms:
0.015625 + -0.25q + q2 = -1.5 + 0.015625

Combine like terms: -1.5 + 0.015625 = -1.484375
0.015625 + -0.25q + q2 = -1.484375

Factor a perfect square on the left side:
(q + -0.125)(q + -0.125) = -1.484375

Can't calculate square root of the right side.

The solution to this equation could not be determined.