s(s+1)=72

Solution for s(s+1)=72 equation:

Simplifying
s(s + 1) = 72

Reorder the terms:
s(1 + s) = 72
(1 * s + s * s) = 72
(1s + s2) = 72

Solving
1s + s2 = 72

Solving for variable 's'.

Reorder the terms:
-72 + 1s + s2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 1s + s2 = 0

Factor a trinomial.
(-9 + -1s)(8 + -1s) = 0

Subproblem 1
Set the factor '(-9 + -1s)' equal to zero and attempt to solve:

Simplifying
-9 + -1s = 0

Solving
-9 + -1s = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1s = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1s = 0 + 9
-1s = 0 + 9

Combine like terms: 0 + 9 = 9
-1s = 9

Divide each side by '-1'.
s = -9

Simplifying
s = -9
Subproblem 2
Set the factor '(8 + -1s)' equal to zero and attempt to solve:

Simplifying
8 + -1s = 0

Solving
8 + -1s = 0

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

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

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

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

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

Simplifying
s = 8
Solution
s = {-9, 8}