(c-6)(c-13)=0

Solution for (c-6)(c-13)=0 equation:

Simplifying
(c + -6)(c + -13) = 0

Reorder the terms:
(-6 + c)(c + -13) = 0

Reorder the terms:
(-6 + c)(-13 + c) = 0

Multiply (-6 + c) * (-13 + c)
(-6(-13 + c) + c(-13 + c)) = 0
((-13 * -6 + c * -6) + c(-13 + c)) = 0
((78 + -6c) + c(-13 + c)) = 0
(78 + -6c + (-13 * c + c * c)) = 0
(78 + -6c + (-13c + c2)) = 0

Combine like terms: -6c + -13c = -19c
(78 + -19c + c2) = 0

Solving
78 + -19c + c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(6 + -1c)(13 + -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 '(13 + -1c)' equal to zero and attempt to solve:

Simplifying
13 + -1c = 0

Solving
13 + -1c = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1c = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1c = 0 + -13
-1c = 0 + -13

Combine like terms: 0 + -13 = -13
-1c = -13

Divide each side by '-1'.
c = 13

Simplifying
c = 13
Solution
c = {6, 13}