(r-8)x(r+3)=

Solution for (r-8)x(r+3)= equation:

Simplifying
(r + -8) * x(r + 3) = 0

Reorder the terms:
(-8 + r) * x(r + 3) = 0

Reorder the terms:
(-8 + r) * x(3 + r) = 0

Reorder the terms for easier multiplication:
x(-8 + r)(3 + r) = 0

Multiply (-8 + r) * (3 + r)
x(-8(3 + r) + r(3 + r)) = 0
x((3 * -8 + r * -8) + r(3 + r)) = 0
x((-24 + -8r) + r(3 + r)) = 0
x(-24 + -8r + (3 * r + r * r)) = 0
x(-24 + -8r + (3r + r2)) = 0

Combine like terms: -8r + 3r = -5r
x(-24 + -5r + r2) = 0
(-24 * x + -5r * x + r2 * x) = 0

Reorder the terms:
(-5rx + r2x + -24x) = 0
(-5rx + r2x + -24x) = 0

Solving
-5rx + r2x + -24x = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5r + r2 + -24) = 0

Factor a trinomial.
x((r + -8)(r + 3)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(r + -8)' equal to zero and attempt to solve:

Simplifying
r + -8 = 0

Reorder the terms:
-8 + r = 0

Solving
-8 + r = 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 + r = 0 + 8

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

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

Simplifying
r = 8
Subproblem 3
Set the factor '(r + 3)' equal to zero and attempt to solve:

Simplifying
r + 3 = 0

Reorder the terms:
3 + r = 0

Solving
3 + r = 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 + r = 0 + -3

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

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

Simplifying
r = -3
Solution
r = {8, -3}