(r+4)(6r-9)=0

Solution for (r+4)(6r-9)=0 equation:

Simplifying
(r + 4)(6r + -9) = 0

Reorder the terms:
(4 + r)(6r + -9) = 0

Reorder the terms:
(4 + r)(-9 + 6r) = 0

Multiply (4 + r) * (-9 + 6r)
(4(-9 + 6r) + r(-9 + 6r)) = 0
((-9 * 4 + 6r * 4) + r(-9 + 6r)) = 0
((-36 + 24r) + r(-9 + 6r)) = 0
(-36 + 24r + (-9 * r + 6r * r)) = 0
(-36 + 24r + (-9r + 6r2)) = 0

Combine like terms: 24r + -9r = 15r
(-36 + 15r + 6r2) = 0

Solving
-36 + 15r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 5r + 2r2) = 0

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

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

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
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 = {-4, 1.5}