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

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

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

Reorder the terms:
4(5 + c)(-2) * c = 12

Reorder the terms for easier multiplication:
4 * -2c(5 + c) = 12

Multiply 4 * -2
-8c(5 + c) = 12
(5 * -8c + c * -8c) = 12
(-40c + -8c2) = 12

Solving
-40c + -8c2 = 12

Solving for variable 'c'.

Reorder the terms:
-12 + -40c + -8c2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -40c + -8c2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(3 + 10c + 2c2) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(3 + 10c + 2c2)' equal to zero and attempt to solve:

Simplifying
3 + 10c + 2c2 = 0

Solving
3 + 10c + 2c2 = 0

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

Divide each side by '2'.
1.5 + 5c + c2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 5c + -1.5 + c2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 5c + c2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 5c + c2 = 0 + -1.5
5c + c2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
5c + c2 = -1.5

The c term is 5c.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5c + 6.25 + c2 = -1.5 + 6.25

Reorder the terms:
6.25 + 5c + c2 = -1.5 + 6.25

Combine like terms: -1.5 + 6.25 = 4.75
6.25 + 5c + c2 = 4.75

Factor a perfect square on the left side:
(c + 2.5)(c + 2.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(c + 2.5) equal to 2.179449472 and -2.179449472.

Subproblem 1
c + 2.5 = 2.179449472

Simplifying
c + 2.5 = 2.179449472

Reorder the terms:
2.5 + c = 2.179449472

Solving
2.5 + c = 2.179449472

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = 2.179449472 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = 2.179449472 + -2.5
c = 2.179449472 + -2.5

Combine like terms: 2.179449472 + -2.5 = -0.320550528
c = -0.320550528

Simplifying
c = -0.320550528

Subproblem 2
c + 2.5 = -2.179449472

Simplifying
c + 2.5 = -2.179449472

Reorder the terms:
2.5 + c = -2.179449472

Solving
2.5 + c = -2.179449472

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = -2.179449472 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = -2.179449472 + -2.5
c = -2.179449472 + -2.5

Combine like terms: -2.179449472 + -2.5 = -4.679449472
c = -4.679449472

Simplifying
c = -4.679449472

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.320550528, -4.679449472}
Solution
c = {-0.320550528, -4.679449472}