-3c(-c-6)=-3c-6

Solution for -3c(-c-6)=-3c-6 equation:

Simplifying
-3c(-1c + -6) = -3c + -6

Reorder the terms:
-3c(-6 + -1c) = -3c + -6
(-6 * -3c + -1c * -3c) = -3c + -6
(18c + 3c2) = -3c + -6

Reorder the terms:
18c + 3c2 = -6 + -3c

Solving
18c + 3c2 = -6 + -3c

Solving for variable 'c'.

Reorder the terms:
6 + 18c + 3c + 3c2 = -6 + -3c + 6 + 3c

Combine like terms: 18c + 3c = 21c
6 + 21c + 3c2 = -6 + -3c + 6 + 3c

Reorder the terms:
6 + 21c + 3c2 = -6 + 6 + -3c + 3c

Combine like terms: -6 + 6 = 0
6 + 21c + 3c2 = 0 + -3c + 3c
6 + 21c + 3c2 = -3c + 3c

Combine like terms: -3c + 3c = 0
6 + 21c + 3c2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 7c + c2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + 7c + c2)' equal to zero and attempt to solve:

Simplifying
2 + 7c + c2 = 0

Solving
2 + 7c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 7c + -2 + c2 = 0 + -2

Reorder the terms:
2 + -2 + 7c + c2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7c + c2 = 0 + -2
7c + c2 = 0 + -2

Combine like terms: 0 + -2 = -2
7c + c2 = -2

The c term is 7c.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7c + 12.25 + c2 = -2 + 12.25

Reorder the terms:
12.25 + 7c + c2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + 7c + c2 = 10.25

Factor a perfect square on the left side:
(c + 3.5)(c + 3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(c + 3.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
c + 3.5 = 3.201562119

Simplifying
c + 3.5 = 3.201562119

Reorder the terms:
3.5 + c = 3.201562119

Solving
3.5 + c = 3.201562119

Solving for variable 'c'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + c = 3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = 3.201562119 + -3.5
c = 3.201562119 + -3.5

Combine like terms: 3.201562119 + -3.5 = -0.298437881
c = -0.298437881

Simplifying
c = -0.298437881

Subproblem 2
c + 3.5 = -3.201562119

Simplifying
c + 3.5 = -3.201562119

Reorder the terms:
3.5 + c = -3.201562119

Solving
3.5 + c = -3.201562119

Solving for variable 'c'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + c = -3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = -3.201562119 + -3.5
c = -3.201562119 + -3.5

Combine like terms: -3.201562119 + -3.5 = -6.701562119
c = -6.701562119

Simplifying
c = -6.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.298437881, -6.701562119}
Solution
c = {-0.298437881, -6.701562119}