(2r+8)(r-9)=0

Solution for (2r+8)(r-9)=0 equation:

Simplifying
(2r + 8)(r + -9) = 0

Reorder the terms:
(8 + 2r)(r + -9) = 0

Reorder the terms:
(8 + 2r)(-9 + r) = 0

Multiply (8 + 2r) * (-9 + r)
(8(-9 + r) + 2r * (-9 + r)) = 0
((-9 * 8 + r * 8) + 2r * (-9 + r)) = 0
((-72 + 8r) + 2r * (-9 + r)) = 0
(-72 + 8r + (-9 * 2r + r * 2r)) = 0
(-72 + 8r + (-18r + 2r2)) = 0

Combine like terms: 8r + -18r = -10r
(-72 + -10r + 2r2) = 0

Solving
-72 + -10r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -5r + r2) = 0

Factor a trinomial.
2((-4 + -1r)(9 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1r)' equal to zero and attempt to solve:

Simplifying
9 + -1r = 0

Solving
9 + -1r = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1r = 0 + -9
-1r = 0 + -9

Combine like terms: 0 + -9 = -9
-1r = -9

Divide each side by '-1'.
r = 9

Simplifying
r = 9
Solution
r = {-4, 9}