r(r+2)=80

Solution for r(r+2)=80 equation:

Simplifying
r(r + 2) = 80

Reorder the terms:
r(2 + r) = 80
(2 * r + r * r) = 80
(2r + r2) = 80

Solving
2r + r2 = 80

Solving for variable 'r'.

Reorder the terms:
-80 + 2r + r2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 2r + r2 = 0

Factor a trinomial.
(-10 + -1r)(8 + -1r) = 0

Subproblem 1
Set the factor '(-10 + -1r)' equal to zero and attempt to solve:

Simplifying
-10 + -1r = 0

Solving
-10 + -1r = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1r = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1r = 0 + 10
-1r = 0 + 10

Combine like terms: 0 + 10 = 10
-1r = 10

Divide each side by '-1'.
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {-10, 8}