(r-4)2(r+8)=0

Solution for (r-4)2(r+8)=0 equation:

Simplifying
(r + -4) * 2(r + 8) = 0

Reorder the terms:
(-4 + r) * 2(r + 8) = 0

Reorder the terms:
(-4 + r) * 2(8 + r) = 0

Reorder the terms for easier multiplication:
2(-4 + r)(8 + r) = 0

Multiply (-4 + r) * (8 + r)
2(-4(8 + r) + r(8 + r)) = 0
2((8 * -4 + r * -4) + r(8 + r)) = 0
2((-32 + -4r) + r(8 + r)) = 0
2(-32 + -4r + (8 * r + r * r)) = 0
2(-32 + -4r + (8r + r2)) = 0

Combine like terms: -4r + 8r = 4r
2(-32 + 4r + r2) = 0
(-32 * 2 + 4r * 2 + r2 * 2) = 0
(-64 + 8r + 2r2) = 0

Solving
-64 + 8r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 4r + r2) = 0

Factor a trinomial.
2((-8 + -1r)(4 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve:

Simplifying
-8 + -1r = 0

Solving
-8 + -1r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1r = 0 + 8
-1r = 0 + 8

Combine like terms: 0 + 8 = 8
-1r = 8

Divide each side by '-1'.
r = -8

Simplifying
r = -8
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 = {-8, 4}