5(3+c)4(c-6)=

Solution for 5(3+c)4(c-6)= equation:

Simplifying
5(3 + c) * 4(c + -6) = 0

Reorder the terms:
5(3 + c) * 4(-6 + c) = 0

Reorder the terms for easier multiplication:
5 * 4(3 + c)(-6 + c) = 0

Multiply 5 * 4
20(3 + c)(-6 + c) = 0

Multiply (3 + c) * (-6 + c)
20(3(-6 + c) + c(-6 + c)) = 0
20((-6 * 3 + c * 3) + c(-6 + c)) = 0
20((-18 + 3c) + c(-6 + c)) = 0
20(-18 + 3c + (-6 * c + c * c)) = 0
20(-18 + 3c + (-6c + c2)) = 0

Combine like terms: 3c + -6c = -3c
20(-18 + -3c + c2) = 0
(-18 * 20 + -3c * 20 + c2 * 20) = 0
(-360 + -60c + 20c2) = 0

Solving
-360 + -60c + 20c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-18 + -3c + c2) = 0

Factor a trinomial.
20((-3 + -1c)(6 + -1c)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-3 + -1c)' equal to zero and attempt to solve:

Simplifying
-3 + -1c = 0

Solving
-3 + -1c = 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 + -1c = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1c = 0 + 3
-1c = 0 + 3

Combine like terms: 0 + 3 = 3
-1c = 3

Divide each side by '-1'.
c = -3

Simplifying
c = -3
Subproblem 2
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
Solution
c = {-3, 6}