(r-5)(2r+1)=0

Solution for (r-5)(2r+1)=0 equation:

Simplifying
(r + -5)(2r + 1) = 0

Reorder the terms:
(-5 + r)(2r + 1) = 0

Reorder the terms:
(-5 + r)(1 + 2r) = 0

Multiply (-5 + r) * (1 + 2r)
(-5(1 + 2r) + r(1 + 2r)) = 0
((1 * -5 + 2r * -5) + r(1 + 2r)) = 0
((-5 + -10r) + r(1 + 2r)) = 0
(-5 + -10r + (1 * r + 2r * r)) = 0
(-5 + -10r + (1r + 2r2)) = 0

Combine like terms: -10r + 1r = -9r
(-5 + -9r + 2r2) = 0

Solving
-5 + -9r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -2r)(5 + -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 '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-0.5, 5}