p(p-1)=12

Solution for p(p-1)=12 equation:

Simplifying
p(p + -1) = 12

Reorder the terms:
p(-1 + p) = 12
(-1 * p + p * p) = 12
(-1p + p2) = 12

Solving
-1p + p2 = 12

Solving for variable 'p'.

Reorder the terms:
-12 + -1p + p2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -1p + p2 = 0

Factor a trinomial.
(-3 + -1p)(4 + -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 '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1p = 0 + -4
-1p = 0 + -4

Combine like terms: 0 + -4 = -4
-1p = -4

Divide each side by '-1'.
p = 4

Simplifying
p = 4
Solution
p = {-3, 4}