(r-4)(r+16)=0

Solution for (r-4)(r+16)=0 equation:

Simplifying
(r + -4)(r + 16) = 0

Reorder the terms:
(-4 + r)(r + 16) = 0

Reorder the terms:
(-4 + r)(16 + r) = 0

Multiply (-4 + r) * (16 + r)
(-4(16 + r) + r(16 + r)) = 0
((16 * -4 + r * -4) + r(16 + r)) = 0
((-64 + -4r) + r(16 + r)) = 0
(-64 + -4r + (16 * r + r * r)) = 0
(-64 + -4r + (16r + r2)) = 0

Combine like terms: -4r + 16r = 12r
(-64 + 12r + r2) = 0

Solving
-64 + 12r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-16 + -1r)(4 + -1r) = 0

Subproblem 1
Set the factor '(-16 + -1r)' equal to zero and attempt to solve:

Simplifying
-16 + -1r = 0

Solving
-16 + -1r = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1r = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1r = 0 + 16
-1r = 0 + 16

Combine like terms: 0 + 16 = 16
-1r = 16

Divide each side by '-1'.
r = -16

Simplifying
r = -16
Subproblem 2
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
Solution
r = {-16, 4}