.25q+2=(-6q+3)4(2q+1)

Solution for .25q+2=(-6q+3)4(2q+1) equation:

Simplifying
0.25q + 2 = (-6q + 3) * 4(2q + 1)

Reorder the terms:
2 + 0.25q = (-6q + 3) * 4(2q + 1)

Reorder the terms:
2 + 0.25q = (3 + -6q) * 4(2q + 1)

Reorder the terms:
2 + 0.25q = (3 + -6q) * 4(1 + 2q)

Reorder the terms for easier multiplication:
2 + 0.25q = 4(3 + -6q)(1 + 2q)

Multiply (3 + -6q) * (1 + 2q)
2 + 0.25q = 4(3(1 + 2q) + -6q * (1 + 2q))
2 + 0.25q = 4((1 * 3 + 2q * 3) + -6q * (1 + 2q))
2 + 0.25q = 4((3 + 6q) + -6q * (1 + 2q))
2 + 0.25q = 4(3 + 6q + (1 * -6q + 2q * -6q))
2 + 0.25q = 4(3 + 6q + (-6q + -12q2))

Combine like terms: 6q + -6q = 0
2 + 0.25q = 4(3 + 0 + -12q2)
2 + 0.25q = 4(3 + -12q2)
2 + 0.25q = (3 * 4 + -12q2 * 4)
2 + 0.25q = (12 + -48q2)

Solving
2 + 0.25q = 12 + -48q2

Solving for variable 'q'.

Reorder the terms:
2 + -12 + 0.25q + 48q2 = 12 + -48q2 + -12 + 48q2

Combine like terms: 2 + -12 = -10
-10 + 0.25q + 48q2 = 12 + -48q2 + -12 + 48q2

Reorder the terms:
-10 + 0.25q + 48q2 = 12 + -12 + -48q2 + 48q2

Combine like terms: 12 + -12 = 0
-10 + 0.25q + 48q2 = 0 + -48q2 + 48q2
-10 + 0.25q + 48q2 = -48q2 + 48q2

Combine like terms: -48q2 + 48q2 = 0
-10 + 0.25q + 48q2 = 0

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

Divide each side by '48'.
-0.2083333333 + 0.005208333333q + q2 = 0

Move the constant term to the right:

Add '0.2083333333' to each side of the equation.
-0.2083333333 + 0.005208333333q + 0.2083333333 + q2 = 0 + 0.2083333333

Reorder the terms:
-0.2083333333 + 0.2083333333 + 0.005208333333q + q2 = 0 + 0.2083333333

Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000
0.0000000000 + 0.005208333333q + q2 = 0 + 0.2083333333
0.005208333333q + q2 = 0 + 0.2083333333

Combine like terms: 0 + 0.2083333333 = 0.2083333333
0.005208333333q + q2 = 0.2083333333

The q term is 0.005208333333q.  Take half its coefficient (0.002604166667).
Square it (0.000006781684030) and add it to both sides.

Add '0.000006781684030' to each side of the equation.
0.005208333333q + 0.000006781684030 + q2 = 0.2083333333 + 0.000006781684030

Reorder the terms:
0.000006781684030 + 0.005208333333q + q2 = 0.2083333333 + 0.000006781684030

Combine like terms: 0.2083333333 + 0.000006781684030 = 0.20834011498403
0.000006781684030 + 0.005208333333q + q2 = 0.20834011498403

Factor a perfect square on the left side:
(q + 0.002604166667)(q + 0.002604166667) = 0.20834011498403

Calculate the square root of the right side: 0.456442893

Break this problem into two subproblems by setting 
(q + 0.002604166667) equal to 0.456442893 and -0.456442893.

Subproblem 1
q + 0.002604166667 = 0.456442893

Simplifying
q + 0.002604166667 = 0.456442893

Reorder the terms:
0.002604166667 + q = 0.456442893

Solving
0.002604166667 + q = 0.456442893

Solving for variable 'q'.

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

Add '-0.002604166667' to each side of the equation.
0.002604166667 + -0.002604166667 + q = 0.456442893 + -0.002604166667

Combine like terms: 0.002604166667 + -0.002604166667 = 0.000000000000
0.000000000000 + q = 0.456442893 + -0.002604166667
q = 0.456442893 + -0.002604166667

Combine like terms: 0.456442893 + -0.002604166667 = 0.453838726333
q = 0.453838726333

Simplifying
q = 0.453838726333

Subproblem 2
q + 0.002604166667 = -0.456442893

Simplifying
q + 0.002604166667 = -0.456442893

Reorder the terms:
0.002604166667 + q = -0.456442893

Solving
0.002604166667 + q = -0.456442893

Solving for variable 'q'.

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

Add '-0.002604166667' to each side of the equation.
0.002604166667 + -0.002604166667 + q = -0.456442893 + -0.002604166667

Combine like terms: 0.002604166667 + -0.002604166667 = 0.000000000000
0.000000000000 + q = -0.456442893 + -0.002604166667
q = -0.456442893 + -0.002604166667

Combine like terms: -0.456442893 + -0.002604166667 = -0.459047059667
q = -0.459047059667

Simplifying
q = -0.459047059667

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.453838726333, -0.459047059667}