(5-p)(4+p)=0

Solution for (5-p)(4+p)=0 equation:

Simplifying
(5 + -1p)(4 + p) = 0

Multiply (5 + -1p) * (4 + p)
(5(4 + p) + -1p * (4 + p)) = 0
((4 * 5 + p * 5) + -1p * (4 + p)) = 0
((20 + 5p) + -1p * (4 + p)) = 0
(20 + 5p + (4 * -1p + p * -1p)) = 0
(20 + 5p + (-4p + -1p2)) = 0

Combine like terms: 5p + -4p = 1p
(20 + 1p + -1p2) = 0

Solving
20 + 1p + -1p2 = 0

Solving for variable 'p'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(4 + p)' equal to zero and attempt to solve:

Simplifying
4 + p = 0

Solving
4 + p = 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 + p = 0 + -4

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

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

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