(p-1)(p-3)=15

Solution for (p-1)(p-3)=15 equation:

Simplifying
(p + -1)(p + -3) = 15

Reorder the terms:
(-1 + p)(p + -3) = 15

Reorder the terms:
(-1 + p)(-3 + p) = 15

Multiply (-1 + p) * (-3 + p)
(-1(-3 + p) + p(-3 + p)) = 15
((-3 * -1 + p * -1) + p(-3 + p)) = 15
((3 + -1p) + p(-3 + p)) = 15
(3 + -1p + (-3 * p + p * p)) = 15
(3 + -1p + (-3p + p2)) = 15

Combine like terms: -1p + -3p = -4p
(3 + -4p + p2) = 15

Solving
3 + -4p + p2 = 15

Solving for variable 'p'.

Reorder the terms:
3 + -15 + -4p + p2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + -4p + p2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + -4p + p2 = 0

Factor a trinomial.
(-2 + -1p)(6 + -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 '(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 = {-2, 6}