4(q-1)16q=3(2-q)-12

Solution for 4(q-1)16q=3(2-q)-12 equation:

Simplifying
4(q + -1) * 16q = 3(2 + -1q) + -12

Reorder the terms:
4(-1 + q) * 16q = 3(2 + -1q) + -12

Reorder the terms for easier multiplication:
4 * 16q(-1 + q) = 3(2 + -1q) + -12

Multiply 4 * 16
64q(-1 + q) = 3(2 + -1q) + -12
(-1 * 64q + q * 64q) = 3(2 + -1q) + -12
(-64q + 64q2) = 3(2 + -1q) + -12
-64q + 64q2 = (2 * 3 + -1q * 3) + -12
-64q + 64q2 = (6 + -3q) + -12

Reorder the terms:
-64q + 64q2 = 6 + -12 + -3q

Combine like terms: 6 + -12 = -6
-64q + 64q2 = -6 + -3q

Solving
-64q + 64q2 = -6 + -3q

Solving for variable 'q'.

Reorder the terms:
6 + -64q + 3q + 64q2 = -6 + -3q + 6 + 3q

Combine like terms: -64q + 3q = -61q
6 + -61q + 64q2 = -6 + -3q + 6 + 3q

Reorder the terms:
6 + -61q + 64q2 = -6 + 6 + -3q + 3q

Combine like terms: -6 + 6 = 0
6 + -61q + 64q2 = 0 + -3q + 3q
6 + -61q + 64q2 = -3q + 3q

Combine like terms: -3q + 3q = 0
6 + -61q + 64q2 = 0

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

Divide each side by '64'.
0.09375 + -0.953125q + q2 = 0

Move the constant term to the right:

Add '-0.09375' to each side of the equation.
0.09375 + -0.953125q + -0.09375 + q2 = 0 + -0.09375

Reorder the terms:
0.09375 + -0.09375 + -0.953125q + q2 = 0 + -0.09375

Combine like terms: 0.09375 + -0.09375 = 0.00000
0.00000 + -0.953125q + q2 = 0 + -0.09375
-0.953125q + q2 = 0 + -0.09375

Combine like terms: 0 + -0.09375 = -0.09375
-0.953125q + q2 = -0.09375

The q term is -0.953125q.  Take half its coefficient (-0.4765625).
Square it (0.2271118164) and add it to both sides.

Add '0.2271118164' to each side of the equation.
-0.953125q + 0.2271118164 + q2 = -0.09375 + 0.2271118164

Reorder the terms:
0.2271118164 + -0.953125q + q2 = -0.09375 + 0.2271118164

Combine like terms: -0.09375 + 0.2271118164 = 0.1333618164
0.2271118164 + -0.953125q + q2 = 0.1333618164

Factor a perfect square on the left side:
(q + -0.4765625)(q + -0.4765625) = 0.1333618164

Calculate the square root of the right side: 0.365187372

Break this problem into two subproblems by setting 
(q + -0.4765625) equal to 0.365187372 and -0.365187372.

Subproblem 1
q + -0.4765625 = 0.365187372

Simplifying
q + -0.4765625 = 0.365187372

Reorder the terms:
-0.4765625 + q = 0.365187372

Solving
-0.4765625 + q = 0.365187372

Solving for variable 'q'.

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

Add '0.4765625' to each side of the equation.
-0.4765625 + 0.4765625 + q = 0.365187372 + 0.4765625

Combine like terms: -0.4765625 + 0.4765625 = 0.0000000
0.0000000 + q = 0.365187372 + 0.4765625
q = 0.365187372 + 0.4765625

Combine like terms: 0.365187372 + 0.4765625 = 0.841749872
q = 0.841749872

Simplifying
q = 0.841749872

Subproblem 2
q + -0.4765625 = -0.365187372

Simplifying
q + -0.4765625 = -0.365187372

Reorder the terms:
-0.4765625 + q = -0.365187372

Solving
-0.4765625 + q = -0.365187372

Solving for variable 'q'.

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

Add '0.4765625' to each side of the equation.
-0.4765625 + 0.4765625 + q = -0.365187372 + 0.4765625

Combine like terms: -0.4765625 + 0.4765625 = 0.0000000
0.0000000 + q = -0.365187372 + 0.4765625
q = -0.365187372 + 0.4765625

Combine like terms: -0.365187372 + 0.4765625 = 0.111375128
q = 0.111375128

Simplifying
q = 0.111375128

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.841749872, 0.111375128}