(12r+9)(5r-15)=0

Solution for (12r+9)(5r-15)=0 equation:

Simplifying
(12r + 9)(5r + -15) = 0

Reorder the terms:
(9 + 12r)(5r + -15) = 0

Reorder the terms:
(9 + 12r)(-15 + 5r) = 0

Multiply (9 + 12r) * (-15 + 5r)
(9(-15 + 5r) + 12r * (-15 + 5r)) = 0
((-15 * 9 + 5r * 9) + 12r * (-15 + 5r)) = 0
((-135 + 45r) + 12r * (-15 + 5r)) = 0
(-135 + 45r + (-15 * 12r + 5r * 12r)) = 0
(-135 + 45r + (-180r + 60r2)) = 0

Combine like terms: 45r + -180r = -135r
(-135 + -135r + 60r2) = 0

Solving
-135 + -135r + 60r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-9 + -9r + 4r2) = 0

Factor a trinomial.
15((-3 + -4r)(3 + -1r)) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-3 + -4r)' equal to zero and attempt to solve:

Simplifying
-3 + -4r = 0

Solving
-3 + -4r = 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 + -4r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4r = 0 + 3
-4r = 0 + 3

Combine like terms: 0 + 3 = 3
-4r = 3

Divide each side by '-4'.
r = -0.75

Simplifying
r = -0.75
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 = {-0.75, 3}