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

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

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

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

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

Multiply (4 + r) * (-1 + r)
(4(-1 + r) + r(-1 + r)) = 0
((-1 * 4 + r * 4) + r(-1 + r)) = 0
((-4 + 4r) + r(-1 + r)) = 0
(-4 + 4r + (-1 * r + r * r)) = 0
(-4 + 4r + (-1r + r2)) = 0

Combine like terms: 4r + -1r = 3r
(-4 + 3r + r2) = 0

Solving
-4 + 3r + r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

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

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

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

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

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

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