(3r-6)(8r+4)=

Solution for (3r-6)(8r+4)= equation:

Simplifying
(3r + -6)(8r + 4) = 0

Reorder the terms:
(-6 + 3r)(8r + 4) = 0

Reorder the terms:
(-6 + 3r)(4 + 8r) = 0

Multiply (-6 + 3r) * (4 + 8r)
(-6(4 + 8r) + 3r * (4 + 8r)) = 0
((4 * -6 + 8r * -6) + 3r * (4 + 8r)) = 0
((-24 + -48r) + 3r * (4 + 8r)) = 0
(-24 + -48r + (4 * 3r + 8r * 3r)) = 0
(-24 + -48r + (12r + 24r2)) = 0

Combine like terms: -48r + 12r = -36r
(-24 + -36r + 24r2) = 0

Solving
-24 + -36r + 24r2 = 0

Solving for variable 'r'.

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

Factor a trinomial.
12((-1 + -2r)(2 + -1r)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-1 + -2r)' equal to zero and attempt to solve:

Simplifying
-1 + -2r = 0

Solving
-1 + -2r = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2r = 0 + 1

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

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

Divide each side by '-2'.
r = -0.5

Simplifying
r = -0.5
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 = {-0.5, 2}