4r^2-4r-48=0

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

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

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

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

Solving for variable 'r'.

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

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

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

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 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 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
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 = {-3, 4}