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

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

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

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

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

Multiply (-3 + 2r) * (5 + 3r)
(-3(5 + 3r) + 2r * (5 + 3r)) = 0
((5 * -3 + 3r * -3) + 2r * (5 + 3r)) = 0
((-15 + -9r) + 2r * (5 + 3r)) = 0
(-15 + -9r + (5 * 2r + 3r * 2r)) = 0
(-15 + -9r + (10r + 6r2)) = 0

Combine like terms: -9r + 10r = 1r
(-15 + 1r + 6r2) = 0

Solving
-15 + 1r + 6r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(-5 + -3r)' equal to zero and attempt to solve:

Simplifying
-5 + -3r = 0

Solving
-5 + -3r = 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 + -3r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3r = 0 + 5
-3r = 0 + 5

Combine like terms: 0 + 5 = 5
-3r = 5

Divide each side by '-3'.
r = -1.666666667

Simplifying
r = -1.666666667
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-1.666666667, 1.5}