c(c+5)=6(c+7)

Solution for c(c+5)=6(c+7) equation:

Simplifying
c(c + 5) = 6(c + 7)

Reorder the terms:
c(5 + c) = 6(c + 7)
(5 * c + c * c) = 6(c + 7)
(5c + c2) = 6(c + 7)

Reorder the terms:
5c + c2 = 6(7 + c)
5c + c2 = (7 * 6 + c * 6)
5c + c2 = (42 + 6c)

Solving
5c + c2 = 42 + 6c

Solving for variable 'c'.

Reorder the terms:
-42 + 5c + -6c + c2 = 42 + 6c + -42 + -6c

Combine like terms: 5c + -6c = -1c
-42 + -1c + c2 = 42 + 6c + -42 + -6c

Reorder the terms:
-42 + -1c + c2 = 42 + -42 + 6c + -6c

Combine like terms: 42 + -42 = 0
-42 + -1c + c2 = 0 + 6c + -6c
-42 + -1c + c2 = 6c + -6c

Combine like terms: 6c + -6c = 0
-42 + -1c + c2 = 0

Factor a trinomial.
(-6 + -1c)(7 + -1c) = 0

Subproblem 1
Set the factor '(-6 + -1c)' equal to zero and attempt to solve:

Simplifying
-6 + -1c = 0

Solving
-6 + -1c = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1c = 0 + 6

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

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

Divide each side by '-1'.
c = -6

Simplifying
c = -6
Subproblem 2
Set the factor '(7 + -1c)' equal to zero and attempt to solve:

Simplifying
7 + -1c = 0

Solving
7 + -1c = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1c = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1c = 0 + -7
-1c = 0 + -7

Combine like terms: 0 + -7 = -7
-1c = -7

Divide each side by '-1'.
c = 7

Simplifying
c = 7
Solution
c = {-6, 7}