5(-3+4c)=4(2c+4)*12c

Solution for 5(-3+4c)=4(2c+4)*12c equation:

Simplifying
5(-3 + 4c) = 4(2c + 4) * 12c
(-3 * 5 + 4c * 5) = 4(2c + 4) * 12c
(-15 + 20c) = 4(2c + 4) * 12c

Reorder the terms:
-15 + 20c = 4(4 + 2c) * 12c

Reorder the terms for easier multiplication:
-15 + 20c = 4 * 12c(4 + 2c)

Multiply 4 * 12
-15 + 20c = 48c(4 + 2c)
-15 + 20c = (4 * 48c + 2c * 48c)
-15 + 20c = (192c + 96c2)

Solving
-15 + 20c = 192c + 96c2

Solving for variable 'c'.

Combine like terms: 20c + -192c = -172c
-15 + -172c + -96c2 = 192c + 96c2 + -192c + -96c2

Reorder the terms:
-15 + -172c + -96c2 = 192c + -192c + 96c2 + -96c2

Combine like terms: 192c + -192c = 0
-15 + -172c + -96c2 = 0 + 96c2 + -96c2
-15 + -172c + -96c2 = 96c2 + -96c2

Combine like terms: 96c2 + -96c2 = 0
-15 + -172c + -96c2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 172c + 96c2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(15 + 172c + 96c2)' equal to zero and attempt to solve:

Simplifying
15 + 172c + 96c2 = 0

Solving
15 + 172c + 96c2 = 0

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

Divide each side by '96'.
0.15625 + 1.791666667c + c2 = 0

Move the constant term to the right:

Add '-0.15625' to each side of the equation.
0.15625 + 1.791666667c + -0.15625 + c2 = 0 + -0.15625

Reorder the terms:
0.15625 + -0.15625 + 1.791666667c + c2 = 0 + -0.15625

Combine like terms: 0.15625 + -0.15625 = 0.00000
0.00000 + 1.791666667c + c2 = 0 + -0.15625
1.791666667c + c2 = 0 + -0.15625

Combine like terms: 0 + -0.15625 = -0.15625
1.791666667c + c2 = -0.15625

The c term is 1.791666667c.  Take half its coefficient (0.8958333335).
Square it (0.8025173614) and add it to both sides.

Add '0.8025173614' to each side of the equation.
1.791666667c + 0.8025173614 + c2 = -0.15625 + 0.8025173614

Reorder the terms:
0.8025173614 + 1.791666667c + c2 = -0.15625 + 0.8025173614

Combine like terms: -0.15625 + 0.8025173614 = 0.6462673614
0.8025173614 + 1.791666667c + c2 = 0.6462673614

Factor a perfect square on the left side:
(c + 0.8958333335)(c + 0.8958333335) = 0.6462673614

Calculate the square root of the right side: 0.803907558

Break this problem into two subproblems by setting 
(c + 0.8958333335) equal to 0.803907558 and -0.803907558.

Subproblem 1
c + 0.8958333335 = 0.803907558

Simplifying
c + 0.8958333335 = 0.803907558

Reorder the terms:
0.8958333335 + c = 0.803907558

Solving
0.8958333335 + c = 0.803907558

Solving for variable 'c'.

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

Add '-0.8958333335' to each side of the equation.
0.8958333335 + -0.8958333335 + c = 0.803907558 + -0.8958333335

Combine like terms: 0.8958333335 + -0.8958333335 = 0.0000000000
0.0000000000 + c = 0.803907558 + -0.8958333335
c = 0.803907558 + -0.8958333335

Combine like terms: 0.803907558 + -0.8958333335 = -0.0919257755
c = -0.0919257755

Simplifying
c = -0.0919257755

Subproblem 2
c + 0.8958333335 = -0.803907558

Simplifying
c + 0.8958333335 = -0.803907558

Reorder the terms:
0.8958333335 + c = -0.803907558

Solving
0.8958333335 + c = -0.803907558

Solving for variable 'c'.

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

Add '-0.8958333335' to each side of the equation.
0.8958333335 + -0.8958333335 + c = -0.803907558 + -0.8958333335

Combine like terms: 0.8958333335 + -0.8958333335 = 0.0000000000
0.0000000000 + c = -0.803907558 + -0.8958333335
c = -0.803907558 + -0.8958333335

Combine like terms: -0.803907558 + -0.8958333335 = -1.6997408915
c = -1.6997408915

Simplifying
c = -1.6997408915

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.0919257755, -1.6997408915}
Solution
c = {-0.0919257755, -1.6997408915}