p^2=6p-5

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

Simplifying
p2 = 6p + -5

Reorder the terms:
p2 = -5 + 6p

Solving
p2 = -5 + 6p

Solving for variable 'p'.

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

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

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

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

Factor a trinomial.
(1 + -1p)(5 + -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 '(5 + -1p)' equal to zero and attempt to solve:

Simplifying
5 + -1p = 0

Solving
5 + -1p = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1p = 0 + -5
-1p = 0 + -5

Combine like terms: 0 + -5 = -5
-1p = -5

Divide each side by '-1'.
p = 5

Simplifying
p = 5
Solution
p = {1, 5}