(p+6)(p-3)=0

Solution for (p+6)(p-3)=0 equation:

Simplifying
(p + 6)(p + -3) = 0

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

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

Multiply (6 + p) * (-3 + p)
(6(-3 + p) + p(-3 + p)) = 0
((-3 * 6 + p * 6) + p(-3 + p)) = 0
((-18 + 6p) + p(-3 + p)) = 0
(-18 + 6p + (-3 * p + p * p)) = 0
(-18 + 6p + (-3p + p2)) = 0

Combine like terms: 6p + -3p = 3p
(-18 + 3p + p2) = 0

Solving
-18 + 3p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-6 + -1p)(3 + -1p) = 0

Subproblem 1
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
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 = {-6, 3}