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.
(-6 + -1p)(1 + -1p) = 0

Subproblem 1
Set the factor '(-6 + -1p)' equal to zero and attempt to solve:

Simplifying
-6 + -1p = 0

Solving
-6 + -1p = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1p = 0 + 6

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

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

Divide each side by '-1'.
p = -6

Simplifying
p = -6
Subproblem 2
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
Solution
p = {-6, 1}