(p-5)(p+2)=0

Solution for (p-5)(p+2)=0 equation:

Simplifying
(p + -5)(p + 2) = 0

Reorder the terms:
(-5 + p)(p + 2) = 0

Reorder the terms:
(-5 + p)(2 + p) = 0

Multiply (-5 + p) * (2 + p)
(-5(2 + p) + p(2 + p)) = 0
((2 * -5 + p * -5) + p(2 + p)) = 0
((-10 + -5p) + p(2 + p)) = 0
(-10 + -5p + (2 * p + p * p)) = 0
(-10 + -5p + (2p + p2)) = 0

Combine like terms: -5p + 2p = -3p
(-10 + -3p + p2) = 0

Solving
-10 + -3p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-2 + -1p)(5 + -1p) = 0

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

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

Simplifying
p = -2
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 = {-2, 5}