11q(2q-8)=-4(7-3q)

Solution for 11q(2q-8)=-4(7-3q) equation:

Simplifying
11q(2q + -8) = -4(7 + -3q)

Reorder the terms:
11q(-8 + 2q) = -4(7 + -3q)
(-8 * 11q + 2q * 11q) = -4(7 + -3q)
(-88q + 22q2) = -4(7 + -3q)
-88q + 22q2 = (7 * -4 + -3q * -4)
-88q + 22q2 = (-28 + 12q)

Solving
-88q + 22q2 = -28 + 12q

Solving for variable 'q'.

Reorder the terms:
28 + -88q + -12q + 22q2 = -28 + 12q + 28 + -12q

Combine like terms: -88q + -12q = -100q
28 + -100q + 22q2 = -28 + 12q + 28 + -12q

Reorder the terms:
28 + -100q + 22q2 = -28 + 28 + 12q + -12q

Combine like terms: -28 + 28 = 0
28 + -100q + 22q2 = 0 + 12q + -12q
28 + -100q + 22q2 = 12q + -12q

Combine like terms: 12q + -12q = 0
28 + -100q + 22q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -50q + 11q2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(14 + -50q + 11q2)' equal to zero and attempt to solve:

Simplifying
14 + -50q + 11q2 = 0

Solving
14 + -50q + 11q2 = 0

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

Divide each side by '11'.
1.272727273 + -4.545454545q + q2 = 0

Move the constant term to the right:

Add '-1.272727273' to each side of the equation.
1.272727273 + -4.545454545q + -1.272727273 + q2 = 0 + -1.272727273

Reorder the terms:
1.272727273 + -1.272727273 + -4.545454545q + q2 = 0 + -1.272727273

Combine like terms: 1.272727273 + -1.272727273 = 0.000000000
0.000000000 + -4.545454545q + q2 = 0 + -1.272727273
-4.545454545q + q2 = 0 + -1.272727273

Combine like terms: 0 + -1.272727273 = -1.272727273
-4.545454545q + q2 = -1.272727273

The q term is -4.545454545q.  Take half its coefficient (-2.272727273).
Square it (5.165289257) and add it to both sides.

Add '5.165289257' to each side of the equation.
-4.545454545q + 5.165289257 + q2 = -1.272727273 + 5.165289257

Reorder the terms:
5.165289257 + -4.545454545q + q2 = -1.272727273 + 5.165289257

Combine like terms: -1.272727273 + 5.165289257 = 3.892561984
5.165289257 + -4.545454545q + q2 = 3.892561984

Factor a perfect square on the left side:
(q + -2.272727273)(q + -2.272727273) = 3.892561984

Calculate the square root of the right side: 1.972957674

Break this problem into two subproblems by setting 
(q + -2.272727273) equal to 1.972957674 and -1.972957674.

Subproblem 1
q + -2.272727273 = 1.972957674

Simplifying
q + -2.272727273 = 1.972957674

Reorder the terms:
-2.272727273 + q = 1.972957674

Solving
-2.272727273 + q = 1.972957674

Solving for variable 'q'.

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

Add '2.272727273' to each side of the equation.
-2.272727273 + 2.272727273 + q = 1.972957674 + 2.272727273

Combine like terms: -2.272727273 + 2.272727273 = 0.000000000
0.000000000 + q = 1.972957674 + 2.272727273
q = 1.972957674 + 2.272727273

Combine like terms: 1.972957674 + 2.272727273 = 4.245684947
q = 4.245684947

Simplifying
q = 4.245684947

Subproblem 2
q + -2.272727273 = -1.972957674

Simplifying
q + -2.272727273 = -1.972957674

Reorder the terms:
-2.272727273 + q = -1.972957674

Solving
-2.272727273 + q = -1.972957674

Solving for variable 'q'.

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

Add '2.272727273' to each side of the equation.
-2.272727273 + 2.272727273 + q = -1.972957674 + 2.272727273

Combine like terms: -2.272727273 + 2.272727273 = 0.000000000
0.000000000 + q = -1.972957674 + 2.272727273
q = -1.972957674 + 2.272727273

Combine like terms: -1.972957674 + 2.272727273 = 0.299769599
q = 0.299769599

Simplifying
q = 0.299769599

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {4.245684947, 0.299769599}
Solution
q = {4.245684947, 0.299769599}