(p+8)(p-5)=14

Solution for (p+8)(p-5)=14 equation:

Simplifying
(p + 8)(p + -5) = 14

Reorder the terms:
(8 + p)(p + -5) = 14

Reorder the terms:
(8 + p)(-5 + p) = 14

Multiply (8 + p) * (-5 + p)
(8(-5 + p) + p(-5 + p)) = 14
((-5 * 8 + p * 8) + p(-5 + p)) = 14
((-40 + 8p) + p(-5 + p)) = 14
(-40 + 8p + (-5 * p + p * p)) = 14
(-40 + 8p + (-5p + p2)) = 14

Combine like terms: 8p + -5p = 3p
(-40 + 3p + p2) = 14

Solving
-40 + 3p + p2 = 14

Solving for variable 'p'.

Reorder the terms:
-40 + -14 + 3p + p2 = 14 + -14

Combine like terms: -40 + -14 = -54
-54 + 3p + p2 = 14 + -14

Combine like terms: 14 + -14 = 0
-54 + 3p + p2 = 0

Factor a trinomial.
(-9 + -1p)(6 + -1p) = 0

Subproblem 1
Set the factor '(-9 + -1p)' equal to zero and attempt to solve:

Simplifying
-9 + -1p = 0

Solving
-9 + -1p = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1p = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1p = 0 + 9
-1p = 0 + 9

Combine like terms: 0 + 9 = 9
-1p = 9

Divide each side by '-1'.
p = -9

Simplifying
p = -9
Subproblem 2
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
Solution
p = {-9, 6}