p^2=5p-6

Solution for p^2=5p-6 equation:

Simplifying
p2 = 5p + -6

Reorder the terms:
p2 = -6 + 5p

Solving
p2 = -6 + 5p

Solving for variable 'p'.

Reorder the terms:
6 + -5p + p2 = -6 + 5p + 6 + -5p

Reorder the terms:
6 + -5p + p2 = -6 + 6 + 5p + -5p

Combine like terms: -6 + 6 = 0
6 + -5p + p2 = 0 + 5p + -5p
6 + -5p + p2 = 5p + -5p

Combine like terms: 5p + -5p = 0
6 + -5p + 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}