(c-4)(c+1)=0

Solution for (c-4)(c+1)=0 equation:

Simplifying
(c + -4)(c + 1) = 0

Reorder the terms:
(-4 + c)(c + 1) = 0

Reorder the terms:
(-4 + c)(1 + c) = 0

Multiply (-4 + c) * (1 + c)
(-4(1 + c) + c(1 + c)) = 0
((1 * -4 + c * -4) + c(1 + c)) = 0
((-4 + -4c) + c(1 + c)) = 0
(-4 + -4c + (1 * c + c * c)) = 0
(-4 + -4c + (1c + c2)) = 0

Combine like terms: -4c + 1c = -3c
(-4 + -3c + c2) = 0

Solving
-4 + -3c + c2 = 0

Solving for variable 'c'.

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

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

Simplifying
-1 + -1c = 0

Solving
-1 + -1c = 0

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

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

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

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

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

Simplifying
c = -1
Subproblem 2
Set the factor '(4 + -1c)' equal to zero and attempt to solve:

Simplifying
4 + -1c = 0

Solving
4 + -1c = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1c = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1c = 0 + -4
-1c = 0 + -4

Combine like terms: 0 + -4 = -4
-1c = -4

Divide each side by '-1'.
c = 4

Simplifying
c = 4
Solution
c = {-1, 4}