(2r+1)(r-8)=0

Solution for (2r+1)(r-8)=0 equation:

Simplifying
(2r + 1)(r + -8) = 0

Reorder the terms:
(1 + 2r)(r + -8) = 0

Reorder the terms:
(1 + 2r)(-8 + r) = 0

Multiply (1 + 2r) * (-8 + r)
(1(-8 + r) + 2r * (-8 + r)) = 0
((-8 * 1 + r * 1) + 2r * (-8 + r)) = 0
((-8 + 1r) + 2r * (-8 + r)) = 0
(-8 + 1r + (-8 * 2r + r * 2r)) = 0
(-8 + 1r + (-16r + 2r2)) = 0

Combine like terms: 1r + -16r = -15r
(-8 + -15r + 2r2) = 0

Solving
-8 + -15r + 2r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-1 + -2r = 0

Solving
-1 + -2r = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2r = 0 + 1
-2r = 0 + 1

Combine like terms: 0 + 1 = 1
-2r = 1

Divide each side by '-2'.
r = -0.5

Simplifying
r = -0.5
Subproblem 2
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
Solution
r = {-0.5, 8}