(r-4)(r+64)=0

Solution for (r-4)(r+64)=0 equation:

Simplifying
(r + -4)(r + 64) = 0

Reorder the terms:
(-4 + r)(r + 64) = 0

Reorder the terms:
(-4 + r)(64 + r) = 0

Multiply (-4 + r) * (64 + r)
(-4(64 + r) + r(64 + r)) = 0
((64 * -4 + r * -4) + r(64 + r)) = 0
((-256 + -4r) + r(64 + r)) = 0
(-256 + -4r + (64 * r + r * r)) = 0
(-256 + -4r + (64r + r2)) = 0

Combine like terms: -4r + 64r = 60r
(-256 + 60r + r2) = 0

Solving
-256 + 60r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-64 + -1r)(4 + -1r) = 0

Subproblem 1
Set the factor '(-64 + -1r)' equal to zero and attempt to solve:

Simplifying
-64 + -1r = 0

Solving
-64 + -1r = 0

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

Add '64' to each side of the equation.
-64 + 64 + -1r = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -1r = 0 + 64
-1r = 0 + 64

Combine like terms: 0 + 64 = 64
-1r = 64

Divide each side by '-1'.
r = -64

Simplifying
r = -64
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 = {-64, 4}