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

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

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

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

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

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

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

Solving
-15 + -1r + 2r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
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
Solution
r = {-2.5, 3}