3(c-5)+4c(c-5)=0

Solution for 3(c-5)+4c(c-5)=0 equation:

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

Reorder the terms:
3(-5 + c) + 4c(c + -5) = 0
(-5 * 3 + c * 3) + 4c(c + -5) = 0
(-15 + 3c) + 4c(c + -5) = 0

Reorder the terms:
-15 + 3c + 4c(-5 + c) = 0
-15 + 3c + (-5 * 4c + c * 4c) = 0
-15 + 3c + (-20c + 4c2) = 0

Combine like terms: 3c + -20c = -17c
-15 + -17c + 4c2 = 0

Solving
-15 + -17c + 4c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-3 + -4c)(5 + -1c) = 0

Subproblem 1
Set the factor '(-3 + -4c)' equal to zero and attempt to solve:

Simplifying
-3 + -4c = 0

Solving
-3 + -4c = 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 + -4c = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4c = 0 + 3
-4c = 0 + 3

Combine like terms: 0 + 3 = 3
-4c = 3

Divide each side by '-4'.
c = -0.75

Simplifying
c = -0.75
Subproblem 2
Set the factor '(5 + -1c)' equal to zero and attempt to solve:

Simplifying
5 + -1c = 0

Solving
5 + -1c = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1c = 0 + -5

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

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

Divide each side by '-1'.
c = 5

Simplifying
c = 5
Solution
c = {-0.75, 5}