p^2-10p+20+1=0

Solution for p^2-10p+20+1=0 equation:

Simplifying
p2 + -10p + 20 + 1 = 0

Reorder the terms:
20 + 1 + -10p + p2 = 0

Combine like terms: 20 + 1 = 21
21 + -10p + p2 = 0

Solving
21 + -10p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(3 + -1p)(7 + -1p) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve:

Simplifying
7 + -1p = 0

Solving
7 + -1p = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1p = 0 + -7
-1p = 0 + -7

Combine like terms: 0 + -7 = -7
-1p = -7

Divide each side by '-1'.
p = 7

Simplifying
p = 7
Solution
p = {3, 7}