(p-1)(p+3)=0

Solution for (p-1)(p+3)=0 equation:

Simplifying
(p + -1)(p + 3) = 0

Reorder the terms:
(-1 + p)(p + 3) = 0

Reorder the terms:
(-1 + p)(3 + p) = 0

Multiply (-1 + p) * (3 + p)
(-1(3 + p) + p(3 + p)) = 0
((3 * -1 + p * -1) + p(3 + p)) = 0
((-3 + -1p) + p(3 + p)) = 0
(-3 + -1p + (3 * p + p * p)) = 0
(-3 + -1p + (3p + p2)) = 0

Combine like terms: -1p + 3p = 2p
(-3 + 2p + p2) = 0

Solving
-3 + 2p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-3 + -1p)(1 + -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 '(1 + -1p)' equal to zero and attempt to solve:

Simplifying
1 + -1p = 0

Solving
1 + -1p = 0

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

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

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

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

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

Simplifying
p = 1
Solution
p = {-3, 1}