(2r+4)(3r-8)=

Solution for (2r+4)(3r-8)= equation:

Simplifying
(2r + 4)(3r + -8) = 0

Reorder the terms:
(4 + 2r)(3r + -8) = 0

Reorder the terms:
(4 + 2r)(-8 + 3r) = 0

Multiply (4 + 2r) * (-8 + 3r)
(4(-8 + 3r) + 2r * (-8 + 3r)) = 0
((-8 * 4 + 3r * 4) + 2r * (-8 + 3r)) = 0
((-32 + 12r) + 2r * (-8 + 3r)) = 0
(-32 + 12r + (-8 * 2r + 3r * 2r)) = 0
(-32 + 12r + (-16r + 6r2)) = 0

Combine like terms: 12r + -16r = -4r
(-32 + -4r + 6r2) = 0

Solving
-32 + -4r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -2r + 3r2) = 0

Factor a trinomial.
2((-2 + -1r)(8 + -3r)) = 0

Ignore the factor 2.
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 '(8 + -3r)' equal to zero and attempt to solve:

Simplifying
8 + -3r = 0

Solving
8 + -3r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3r = 0 + -8
-3r = 0 + -8

Combine like terms: 0 + -8 = -8
-3r = -8

Divide each side by '-3'.
r = 2.666666667

Simplifying
r = 2.666666667
Solution
r = {-2, 2.666666667}