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

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

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

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

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

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

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

Solving
-3 + -2p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-1 + -1p)(3 + -1p) = 0

Subproblem 1
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
Subproblem 2
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
Solution
p = {-1, 3}