6(1+c)=c-c^2

Solution for 6(1+c)=c-c^2 equation:

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

Solving
6 + 6c = c + -1c2

Solving for variable 'c'.

Combine like terms: 6c + -1c = 5c
6 + 5c + c2 = c + -1c2 + -1c + c2

Reorder the terms:
6 + 5c + c2 = c + -1c + -1c2 + c2

Combine like terms: c + -1c = 0
6 + 5c + c2 = 0 + -1c2 + c2
6 + 5c + c2 = -1c2 + c2

Combine like terms: -1c2 + c2 = 0
6 + 5c + c2 = 0

Factor a trinomial.
(3 + c)(2 + c) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(2 + c)' equal to zero and attempt to solve:

Simplifying
2 + c = 0

Solving
2 + c = 0

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

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

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

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

Simplifying
c = -2
Solution
c = {-3, -2}