p^2=p+6

Solution for p^2=p+6 equation:

Simplifying
p2 = p + 6

Reorder the terms:
p2 = 6 + p

Solving
p2 = 6 + p

Solving for variable 'p'.

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

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

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
p = {-2, 3}