(4r-5)(3r+6)=0

Solution for (4r-5)(3r+6)=0 equation:

Simplifying
(4r + -5)(3r + 6) = 0

Reorder the terms:
(-5 + 4r)(3r + 6) = 0

Reorder the terms:
(-5 + 4r)(6 + 3r) = 0

Multiply (-5 + 4r) * (6 + 3r)
(-5(6 + 3r) + 4r * (6 + 3r)) = 0
((6 * -5 + 3r * -5) + 4r * (6 + 3r)) = 0
((-30 + -15r) + 4r * (6 + 3r)) = 0
(-30 + -15r + (6 * 4r + 3r * 4r)) = 0
(-30 + -15r + (24r + 12r2)) = 0

Combine like terms: -15r + 24r = 9r
(-30 + 9r + 12r2) = 0

Solving
-30 + 9r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 3r + 4r2) = 0

Factor a trinomial.
3((-2 + -1r)(5 + -4r)) = 0

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

Simplifying
-2 + -1r = 0

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

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

Simplifying
r = -2
Subproblem 2
Set the factor '(5 + -4r)' equal to zero and attempt to solve:

Simplifying
5 + -4r = 0

Solving
5 + -4r = 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 + -4r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4r = 0 + -5
-4r = 0 + -5

Combine like terms: 0 + -5 = -5
-4r = -5

Divide each side by '-4'.
r = 1.25

Simplifying
r = 1.25
Solution
r = {-2, 1.25}