(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 = -7p
(10 + -7p + p2) = 0

Solving
10 + -7p + 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}