5r^2=48+r

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

Simplifying
5r2 = 48 + r

Solving
5r2 = 48 + r

Solving for variable 'r'.

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

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

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

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

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

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 '(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
Solution
r = {-3, 3.2}