24r^2-4r-48=0

Solution for 24r^2-4r-48=0 equation:

Simplifying
24r2 + -4r + -48 = 0

Reorder the terms:
-48 + -4r + 24r2 = 0

Solving
-48 + -4r + 24r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + -1r + 6r2) = 0

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-1.333333333, 1.5}