(3c+7)(c+6)=0

Solution for (3c+7)(c+6)=0 equation:

Simplifying
(3c + 7)(c + 6) = 0

Reorder the terms:
(7 + 3c)(c + 6) = 0

Reorder the terms:
(7 + 3c)(6 + c) = 0

Multiply (7 + 3c) * (6 + c)
(7(6 + c) + 3c * (6 + c)) = 0
((6 * 7 + c * 7) + 3c * (6 + c)) = 0
((42 + 7c) + 3c * (6 + c)) = 0
(42 + 7c + (6 * 3c + c * 3c)) = 0
(42 + 7c + (18c + 3c2)) = 0

Combine like terms: 7c + 18c = 25c
(42 + 25c + 3c2) = 0

Solving
42 + 25c + 3c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(6 + c)(7 + 3c) = 0

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

Simplifying
6 + c = 0

Solving
6 + c = 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 + c = 0 + -6

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

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

Simplifying
c = -6
Subproblem 2
Set the factor '(7 + 3c)' equal to zero and attempt to solve:

Simplifying
7 + 3c = 0

Solving
7 + 3c = 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 + 3c = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3c = 0 + -7
3c = 0 + -7

Combine like terms: 0 + -7 = -7
3c = -7

Divide each side by '3'.
c = -2.333333333

Simplifying
c = -2.333333333
Solution
c = {-6, -2.333333333}