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

Solution for (c+6)(c+1)=-6 equation:

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

Reorder the terms:
(6 + c)(c + 1) = -6

Reorder the terms:
(6 + c)(1 + c) = -6

Multiply (6 + c) * (1 + c)
(6(1 + c) + c(1 + c)) = -6
((1 * 6 + c * 6) + c(1 + c)) = -6
((6 + 6c) + c(1 + c)) = -6
(6 + 6c + (1 * c + c * c)) = -6
(6 + 6c + (1c + c2)) = -6

Combine like terms: 6c + 1c = 7c
(6 + 7c + c2) = -6

Solving
6 + 7c + c2 = -6

Solving for variable 'c'.

Reorder the terms:
6 + 6 + 7c + c2 = -6 + 6

Combine like terms: 6 + 6 = 12
12 + 7c + c2 = -6 + 6

Combine like terms: -6 + 6 = 0
12 + 7c + c2 = 0

Factor a trinomial.
(4 + c)(3 + c) = 0

Subproblem 1
Set the factor '(4 + c)' equal to zero and attempt to solve:

Simplifying
4 + c = 0

Solving
4 + c = 0

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

Add '-4' to each side of the equation.
4 + -4 + c = 0 + -4

Combine like terms: 4 + -4 = 0
0 + c = 0 + -4
c = 0 + -4

Combine like terms: 0 + -4 = -4
c = -4

Simplifying
c = -4
Subproblem 2
Set the factor '(3 + c)' equal to zero and attempt to solve:

Simplifying
3 + c = 0

Solving
3 + c = 0

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

Add '-3' to each side of the equation.
3 + -3 + c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + c = 0 + -3
c = 0 + -3

Combine like terms: 0 + -3 = -3
c = -3

Simplifying
c = -3
Solution
c = {-4, -3}