4r^2-48=-4r

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

Simplifying
4r2 + -48 = -4r

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

Solving
-48 + 4r2 = -4r

Solving for variable 'r'.

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

Combine like terms: -4r + 4r = 0
-48 + 4r + 4r2 = 0

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

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

Ignore the factor 4.
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 '(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
Solution
r = {-4, 3}