8(r+6)(r-4)=0

Solution for 8(r+6)(r-4)=0 equation:

Simplifying
8(r + 6)(r + -4) = 0

Reorder the terms:
8(6 + r)(r + -4) = 0

Reorder the terms:
8(6 + r)(-4 + r) = 0

Multiply (6 + r) * (-4 + r)
8(6(-4 + r) + r(-4 + r)) = 0
8((-4 * 6 + r * 6) + r(-4 + r)) = 0
8((-24 + 6r) + r(-4 + r)) = 0
8(-24 + 6r + (-4 * r + r * r)) = 0
8(-24 + 6r + (-4r + r2)) = 0

Combine like terms: 6r + -4r = 2r
8(-24 + 2r + r2) = 0
(-24 * 8 + 2r * 8 + r2 * 8) = 0
(-192 + 16r + 8r2) = 0

Solving
-192 + 16r + 8r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-24 + 2r + r2) = 0

Factor a trinomial.
8((-6 + -1r)(4 + -1r)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
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 = {-6, 4}