5r^2=30+5r

Solution for 5r^2=30+5r equation:

Simplifying
5r2 = 30 + 5r

Solving
5r2 = 30 + 5r

Solving for variable 'r'.

Reorder the terms:
-30 + -5r + 5r2 = 30 + 5r + -30 + -5r

Reorder the terms:
-30 + -5r + 5r2 = 30 + -30 + 5r + -5r

Combine like terms: 30 + -30 = 0
-30 + -5r + 5r2 = 0 + 5r + -5r
-30 + -5r + 5r2 = 5r + -5r

Combine like terms: 5r + -5r = 0
-30 + -5r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -1r + r2) = 0

Factor a trinomial.
5((-2 + -1r)(3 + -1r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-2 + -1r)' equal to zero and attempt to solve:

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

Simplifying
r = -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 = {-2, 3}