p(p+1)=72

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

Simplifying
p(p + 1) = 72

Reorder the terms:
p(1 + p) = 72
(1 * p + p * p) = 72
(1p + p2) = 72

Solving
1p + p2 = 72

Solving for variable 'p'.

Reorder the terms:
-72 + 1p + p2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 1p + p2 = 0

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

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

Simplifying
-9 + -1p = 0

Solving
-9 + -1p = 0

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

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

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

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

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

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

Simplifying
8 + -1p = 0

Solving
8 + -1p = 0

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

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

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

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

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

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