(p-3)(p-5)=

Solution for (p-3)(p-5)= equation:

Simplifying
(p + -3)(p + -5) = 0

Reorder the terms:
(-3 + p)(p + -5) = 0

Reorder the terms:
(-3 + p)(-5 + p) = 0

Multiply (-3 + p) * (-5 + p)
(-3(-5 + p) + p(-5 + p)) = 0
((-5 * -3 + p * -3) + p(-5 + p)) = 0
((15 + -3p) + p(-5 + p)) = 0
(15 + -3p + (-5 * p + p * p)) = 0
(15 + -3p + (-5p + p2)) = 0

Combine like terms: -3p + -5p = -8p
(15 + -8p + p2) = 0

Solving
15 + -8p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(3 + -1p)(5 + -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 '(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 = {3, 5}