p(p+1)=6

Solution for p(p+1)=6 equation:

Simplifying
p(p + 1) = 6

Reorder the terms:
p(1 + p) = 6
(1 * p + p * p) = 6
(1p + p2) = 6

Solving
1p + p2 = 6

Solving for variable 'p'.

Reorder the terms:
-6 + 1p + p2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 1p + p2 = 0

Factor a trinomial.
(-3 + -1p)(2 + -1p) = 0

Subproblem 1
Set the factor '(-3 + -1p)' equal to zero and attempt to solve:

Simplifying
-3 + -1p = 0

Solving
-3 + -1p = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1p = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1p = 0 + 3
-1p = 0 + 3

Combine like terms: 0 + 3 = 3
-1p = 3

Divide each side by '-1'.
p = -3

Simplifying
p = -3
Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {-3, 2}