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

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

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

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

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

Multiply (-3 + 2r) * (2 + 3r)
(-3(2 + 3r) + 2r * (2 + 3r)) = 0
((2 * -3 + 3r * -3) + 2r * (2 + 3r)) = 0
((-6 + -9r) + 2r * (2 + 3r)) = 0
(-6 + -9r + (2 * 2r + 3r * 2r)) = 0
(-6 + -9r + (4r + 6r2)) = 0

Combine like terms: -9r + 4r = -5r
(-6 + -5r + 6r2) = 0

Solving
-6 + -5r + 6r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(-2 + -3r)' equal to zero and attempt to solve:

Simplifying
-2 + -3r = 0

Solving
-2 + -3r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3r = 0 + 2

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

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

Divide each side by '-3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
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 = {-0.6666666667, 1.5}