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

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

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

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

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

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

Combine like terms: -30r + 12r = -18r
(-24 + -18r + 15r2) = 0

Solving
-24 + -18r + 15r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -6r + 5r2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -5r)' equal to zero and attempt to solve:

Simplifying
-4 + -5r = 0

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

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

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

Divide each side by '-5'.
r = -0.8

Simplifying
r = -0.8
Subproblem 2
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
Solution
r = {-0.8, 2}