(r+5)(r-1)=16

Solution for (r+5)(r-1)=16 equation:

Simplifying
(r + 5)(r + -1) = 16

Reorder the terms:
(5 + r)(r + -1) = 16

Reorder the terms:
(5 + r)(-1 + r) = 16

Multiply (5 + r) * (-1 + r)
(5(-1 + r) + r(-1 + r)) = 16
((-1 * 5 + r * 5) + r(-1 + r)) = 16
((-5 + 5r) + r(-1 + r)) = 16
(-5 + 5r + (-1 * r + r * r)) = 16
(-5 + 5r + (-1r + r2)) = 16

Combine like terms: 5r + -1r = 4r
(-5 + 4r + r2) = 16

Solving
-5 + 4r + r2 = 16

Solving for variable 'r'.

Reorder the terms:
-5 + -16 + 4r + r2 = 16 + -16

Combine like terms: -5 + -16 = -21
-21 + 4r + r2 = 16 + -16

Combine like terms: 16 + -16 = 0
-21 + 4r + r2 = 0

Factor a trinomial.
(-7 + -1r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-7 + -1r)' equal to zero and attempt to solve:

Simplifying
-7 + -1r = 0

Solving
-7 + -1r = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1r = 0 + 7
-1r = 0 + 7

Combine like terms: 0 + 7 = 7
-1r = 7

Divide each side by '-1'.
r = -7

Simplifying
r = -7
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

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

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

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

Simplifying
r = 3
Solution
r = {-7, 3}