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

Solution for (r-4)(3r+8)=0 equation:

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

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

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

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

Combine like terms: -12r + 8r = -4r
(-32 + -4r + 3r2) = 0

Solving
-32 + -4r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-8 + -3r)(4 + -1r) = 0

Subproblem 1
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
Subproblem 2
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
Solution
r = {-2.666666667, 4}