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

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

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

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

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

Multiply (8 + 2r) * (-4 + 3r)
(8(-4 + 3r) + 2r * (-4 + 3r)) = 0
((-4 * 8 + 3r * 8) + 2r * (-4 + 3r)) = 0
((-32 + 24r) + 2r * (-4 + 3r)) = 0
(-32 + 24r + (-4 * 2r + 3r * 2r)) = 0
(-32 + 24r + (-8r + 6r2)) = 0

Combine like terms: 24r + -8r = 16r
(-32 + 16r + 6r2) = 0

Solving
-32 + 16r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 8r + 3r2) = 0

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

Ignore the factor 2.
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 '(4 + -3r)' equal to zero and attempt to solve:

Simplifying
4 + -3r = 0

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

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

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

Divide each side by '-3'.
r = 1.333333333

Simplifying
r = 1.333333333
Solution
r = {-4, 1.333333333}