r+4=r(r+1)

Solution for r+4=r(r+1) equation:

Simplifying
r + 4 = r(r + 1)

Reorder the terms:
4 + r = r(r + 1)

Reorder the terms:
4 + r = r(1 + r)
4 + r = (1 * r + r * r)
4 + r = (1r + r2)

Solving
4 + r = 1r + r2

Solving for variable 'r'.

Combine like terms: r + -1r = 0
4 + 0 + -1r2 = 1r + r2 + -1r + -1r2
4 + -1r2 = 1r + r2 + -1r + -1r2

Reorder the terms:
4 + -1r2 = 1r + -1r + r2 + -1r2

Combine like terms: 1r + -1r = 0
4 + -1r2 = 0 + r2 + -1r2
4 + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
4 + -1r2 = 0

Factor a difference between two squares.
(2 + r)(2 + -1r) = 0

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

Simplifying
2 + r = 0

Solving
2 + r = 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 + r = 0 + -2

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

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

Simplifying
r = -2
Subproblem 2
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
Solution
r = {-2, 2}