(p+1)(p-4)=14

Solution for (p+1)(p-4)=14 equation:

Simplifying
(p + 1)(p + -4) = 14

Reorder the terms:
(1 + p)(p + -4) = 14

Reorder the terms:
(1 + p)(-4 + p) = 14

Multiply (1 + p) * (-4 + p)
(1(-4 + p) + p(-4 + p)) = 14
((-4 * 1 + p * 1) + p(-4 + p)) = 14
((-4 + 1p) + p(-4 + p)) = 14
(-4 + 1p + (-4 * p + p * p)) = 14
(-4 + 1p + (-4p + p2)) = 14

Combine like terms: 1p + -4p = -3p
(-4 + -3p + p2) = 14

Solving
-4 + -3p + p2 = 14

Solving for variable 'p'.

Reorder the terms:
-4 + -14 + -3p + p2 = 14 + -14

Combine like terms: -4 + -14 = -18
-18 + -3p + p2 = 14 + -14

Combine like terms: 14 + -14 = 0
-18 + -3p + p2 = 0

Factor a trinomial.
(-3 + -1p)(6 + -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 '(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 = {-3, 6}