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

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

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

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

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

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

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

Solving
-9 + -9r + 10r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-3 + -5r = 0

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

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

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

Divide each side by '-5'.
r = -0.6

Simplifying
r = -0.6
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 = {-0.6, 1.5}