p^2-p-27=-7

Solution for p^2-p-27=-7 equation:

Simplifying
p2 + -1p + -27 = -7

Reorder the terms:
-27 + -1p + p2 = -7

Solving
-27 + -1p + p2 = -7

Solving for variable 'p'.

Reorder the terms:
-27 + 7 + -1p + p2 = -7 + 7

Combine like terms: -27 + 7 = -20
-20 + -1p + p2 = -7 + 7

Combine like terms: -7 + 7 = 0
-20 + -1p + p2 = 0

Factor a trinomial.
(-4 + -1p)(5 + -1p) = 0

Subproblem 1
Set the factor '(-4 + -1p)' equal to zero and attempt to solve:

Simplifying
-4 + -1p = 0

Solving
-4 + -1p = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1p = 0 + 4
-1p = 0 + 4

Combine like terms: 0 + 4 = 4
-1p = 4

Divide each side by '-1'.
p = -4

Simplifying
p = -4
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 = {-4, 5}