5r^2-48=-r

Solution for 5r^2-48=-r equation:

Simplifying
5r2 + -48 = -1r

Reorder the terms:
-48 + 5r2 = -1r

Solving
-48 + 5r2 = -1r

Solving for variable 'r'.

Reorder the terms:
-48 + r + 5r2 = -1r + r

Combine like terms: -1r + r = 0
-48 + r + 5r2 = 0

Factor a trinomial.
(-16 + -5r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-16 + -5r)' equal to zero and attempt to solve:

Simplifying
-16 + -5r = 0

Solving
-16 + -5r = 0

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

Add '16' to each side of the equation.
-16 + 16 + -5r = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -5r = 0 + 16
-5r = 0 + 16

Combine like terms: 0 + 16 = 16
-5r = 16

Divide each side by '-5'.
r = -3.2

Simplifying
r = -3.2
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 = {-3.2, 3}