p^2=11p+12

Solution for p^2=11p+12 equation:

Simplifying
p2 = 11p + 12

Reorder the terms:
p2 = 12 + 11p

Solving
p2 = 12 + 11p

Solving for variable 'p'.

Reorder the terms:
-12 + -11p + p2 = 12 + 11p + -12 + -11p

Reorder the terms:
-12 + -11p + p2 = 12 + -12 + 11p + -11p

Combine like terms: 12 + -12 = 0
-12 + -11p + p2 = 0 + 11p + -11p
-12 + -11p + p2 = 11p + -11p

Combine like terms: 11p + -11p = 0
-12 + -11p + p2 = 0

Factor a trinomial.
(-1 + -1p)(12 + -1p) = 0

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

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 0

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

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

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

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

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

Simplifying
p = -1
Subproblem 2
Set the factor '(12 + -1p)' equal to zero and attempt to solve:

Simplifying
12 + -1p = 0

Solving
12 + -1p = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1p = 0 + -12

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

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

Divide each side by '-1'.
p = 12

Simplifying
p = 12
Solution
p = {-1, 12}