r^2+4r=5r+30

Solution for r^2+4r=5r+30 equation:

Simplifying
r2 + 4r = 5r + 30

Reorder the terms:
4r + r2 = 5r + 30

Reorder the terms:
4r + r2 = 30 + 5r

Solving
4r + r2 = 30 + 5r

Solving for variable 'r'.

Reorder the terms:
-30 + 4r + -5r + r2 = 30 + 5r + -30 + -5r

Combine like terms: 4r + -5r = -1r
-30 + -1r + r2 = 30 + 5r + -30 + -5r

Reorder the terms:
-30 + -1r + r2 = 30 + -30 + 5r + -5r

Combine like terms: 30 + -30 = 0
-30 + -1r + r2 = 0 + 5r + -5r
-30 + -1r + r2 = 5r + -5r

Combine like terms: 5r + -5r = 0
-30 + -1r + r2 = 0

Factor a trinomial.
(-5 + -1r)(6 + -1r) = 0

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

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1r = 0 + 5

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

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

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-5, 6}