(p-6)(2p+3)=0

Solution for (p-6)(2p+3)=0 equation:

Simplifying
(p + -6)(2p + 3) = 0

Reorder the terms:
(-6 + p)(2p + 3) = 0

Reorder the terms:
(-6 + p)(3 + 2p) = 0

Multiply (-6 + p) * (3 + 2p)
(-6(3 + 2p) + p(3 + 2p)) = 0
((3 * -6 + 2p * -6) + p(3 + 2p)) = 0
((-18 + -12p) + p(3 + 2p)) = 0
(-18 + -12p + (3 * p + 2p * p)) = 0
(-18 + -12p + (3p + 2p2)) = 0

Combine like terms: -12p + 3p = -9p
(-18 + -9p + 2p2) = 0

Solving
-18 + -9p + 2p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-3 + -2p)(6 + -1p) = 0

Subproblem 1
Set the factor '(-3 + -2p)' equal to zero and attempt to solve:

Simplifying
-3 + -2p = 0

Solving
-3 + -2p = 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 + -2p = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2p = 0 + 3
-2p = 0 + 3

Combine like terms: 0 + 3 = 3
-2p = 3

Divide each side by '-2'.
p = -1.5

Simplifying
p = -1.5
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 = {-1.5, 6}