.6(6c-18).75(8c+32)=-18

Solution for .6(6c-18).75(8c+32)=-18 equation:

Simplifying
0.6(6c + -18) * 0.75(8c + 32) = -18

Reorder the terms:
0.6(-18 + 6c) * 0.75(8c + 32) = -18

Reorder the terms:
0.6(-18 + 6c) * 0.75(32 + 8c) = -18

Reorder the terms for easier multiplication:
0.6 * 0.75(-18 + 6c)(32 + 8c) = -18

Multiply 0.6 * 0.75
0.45(-18 + 6c)(32 + 8c) = -18

Multiply (-18 + 6c) * (32 + 8c)
0.45(-18(32 + 8c) + 6c * (32 + 8c)) = -18
0.45((32 * -18 + 8c * -18) + 6c * (32 + 8c)) = -18
0.45((-576 + -144c) + 6c * (32 + 8c)) = -18
0.45(-576 + -144c + (32 * 6c + 8c * 6c)) = -18
0.45(-576 + -144c + (192c + 48c2)) = -18

Combine like terms: -144c + 192c = 48c
0.45(-576 + 48c + 48c2) = -18
(-576 * 0.45 + 48c * 0.45 + 48c2 * 0.45) = -18
(-259.2 + 21.6c + 21.6c2) = -18

Solving
-259.2 + 21.6c + 21.6c2 = -18

Solving for variable 'c'.

Reorder the terms:
-259.2 + 18 + 21.6c + 21.6c2 = -18 + 18

Combine like terms: -259.2 + 18 = -241.2
-241.2 + 21.6c + 21.6c2 = -18 + 18

Combine like terms: -18 + 18 = 0
-241.2 + 21.6c + 21.6c2 = 0

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

Divide each side by '21.6'.
-11.16666667 + c + c2 = 0

Move the constant term to the right:

Add '11.16666667' to each side of the equation.
-11.16666667 + c + 11.16666667 + c2 = 0 + 11.16666667

Reorder the terms:
-11.16666667 + 11.16666667 + c + c2 = 0 + 11.16666667

Combine like terms: -11.16666667 + 11.16666667 = 0.00000000
0.00000000 + c + c2 = 0 + 11.16666667
c + c2 = 0 + 11.16666667

Combine like terms: 0 + 11.16666667 = 11.16666667
c + c2 = 11.16666667

The c term is c.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + c2 = 11.16666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + c2 = 11.16666667 + 0.25

Combine like terms: 11.16666667 + 0.25 = 11.41666667
1.25 + c2 = 11.41666667

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 11.41666667

Calculate the square root of the right side: 3.378855823

Break this problem into two subproblems by setting 
(c + 0.5) equal to 3.378855823 and -3.378855823.

Subproblem 1
c + 0.5 = 3.378855823

Simplifying
c + 0.5 = 3.378855823

Reorder the terms:
0.5 + c = 3.378855823

Solving
0.5 + c = 3.378855823

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = 3.378855823 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 3.378855823 + -0.5
c = 3.378855823 + -0.5

Combine like terms: 3.378855823 + -0.5 = 2.878855823
c = 2.878855823

Simplifying
c = 2.878855823

Subproblem 2
c + 0.5 = -3.378855823

Simplifying
c + 0.5 = -3.378855823

Reorder the terms:
0.5 + c = -3.378855823

Solving
0.5 + c = -3.378855823

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = -3.378855823 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -3.378855823 + -0.5
c = -3.378855823 + -0.5

Combine like terms: -3.378855823 + -0.5 = -3.878855823
c = -3.878855823

Simplifying
c = -3.878855823

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {2.878855823, -3.878855823}