r(r+2)=288

Solution for r(r+2)=288 equation:

Simplifying
r(r + 2) = 288

Reorder the terms:
r(2 + r) = 288
(2 * r + r * r) = 288
(2r + r2) = 288

Solving
2r + r2 = 288

Solving for variable 'r'.

Reorder the terms:
-288 + 2r + r2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + 2r + r2 = 0

Factor a trinomial.
(-18 + -1r)(16 + -1r) = 0

Subproblem 1
Set the factor '(-18 + -1r)' equal to zero and attempt to solve:

Simplifying
-18 + -1r = 0

Solving
-18 + -1r = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1r = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1r = 0 + 18
-1r = 0 + 18

Combine like terms: 0 + 18 = 18
-1r = 18

Divide each side by '-1'.
r = -18

Simplifying
r = -18
Subproblem 2
Set the factor '(16 + -1r)' equal to zero and attempt to solve:

Simplifying
16 + -1r = 0

Solving
16 + -1r = 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 + -1r = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1r = 0 + -16
-1r = 0 + -16

Combine like terms: 0 + -16 = -16
-1r = -16

Divide each side by '-1'.
r = 16

Simplifying
r = 16
Solution
r = {-18, 16}