(2r-5)(r+3)=0

Solution for (2r-5)(r+3)=0 equation:

Simplifying
(2r + -5)(r + 3) = 0

Reorder the terms:
(-5 + 2r)(r + 3) = 0

Reorder the terms:
(-5 + 2r)(3 + r) = 0

Multiply (-5 + 2r) * (3 + r)
(-5(3 + r) + 2r * (3 + r)) = 0
((3 * -5 + r * -5) + 2r * (3 + r)) = 0
((-15 + -5r) + 2r * (3 + r)) = 0
(-15 + -5r + (3 * 2r + r * 2r)) = 0
(-15 + -5r + (6r + 2r2)) = 0

Combine like terms: -5r + 6r = 1r
(-15 + 1r + 2r2) = 0

Solving
-15 + 1r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-3 + -1r)(5 + -2r) = 0

Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 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 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(5 + -2r)' equal to zero and attempt to solve:

Simplifying
5 + -2r = 0

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

Combine like terms: 5 + -5 = 0
0 + -2r = 0 + -5
-2r = 0 + -5

Combine like terms: 0 + -5 = -5
-2r = -5

Divide each side by '-2'.
r = 2.5

Simplifying
r = 2.5
Solution
r = {-3, 2.5}