p^2-2p-53=-5

Solution for p^2-2p-53=-5 equation:

Simplifying
p2 + -2p + -53 = -5

Reorder the terms:
-53 + -2p + p2 = -5

Solving
-53 + -2p + p2 = -5

Solving for variable 'p'.

Reorder the terms:
-53 + 5 + -2p + p2 = -5 + 5

Combine like terms: -53 + 5 = -48
-48 + -2p + p2 = -5 + 5

Combine like terms: -5 + 5 = 0
-48 + -2p + p2 = 0

Factor a trinomial.
(-6 + -1p)(8 + -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 '(8 + -1p)' equal to zero and attempt to solve:

Simplifying
8 + -1p = 0

Solving
8 + -1p = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1p = 0 + -8
-1p = 0 + -8

Combine like terms: 0 + -8 = -8
-1p = -8

Divide each side by '-1'.
p = 8

Simplifying
p = 8
Solution
p = {-6, 8}