p^2-4p+1=6

Solution for p^2-4p+1=6 equation:

Simplifying
p2 + -4p + 1 = 6

Reorder the terms:
1 + -4p + p2 = 6

Solving
1 + -4p + p2 = 6

Solving for variable 'p'.

Reorder the terms:
1 + -6 + -4p + p2 = 6 + -6

Combine like terms: 1 + -6 = -5
-5 + -4p + p2 = 6 + -6

Combine like terms: 6 + -6 = 0
-5 + -4p + 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}