(p-2)(p+3)=0

Solution for (p-2)(p+3)=0 equation:

Simplifying
(p + -2)(p + 3) = 0

Reorder the terms:
(-2 + p)(p + 3) = 0

Reorder the terms:
(-2 + p)(3 + p) = 0

Multiply (-2 + p) * (3 + p)
(-2(3 + p) + p(3 + p)) = 0
((3 * -2 + p * -2) + p(3 + p)) = 0
((-6 + -2p) + p(3 + p)) = 0
(-6 + -2p + (3 * p + p * p)) = 0
(-6 + -2p + (3p + p2)) = 0

Combine like terms: -2p + 3p = 1p
(-6 + 1p + p2) = 0

Solving
-6 + 1p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-3 + -1p)(2 + -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 '(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
Solution
p = {-3, 2}