(3p+8)(2p-3)=0

Solution for (3p+8)(2p-3)=0 equation:

Simplifying
(3p + 8)(2p + -3) = 0

Reorder the terms:
(8 + 3p)(2p + -3) = 0

Reorder the terms:
(8 + 3p)(-3 + 2p) = 0

Multiply (8 + 3p) * (-3 + 2p)
(8(-3 + 2p) + 3p * (-3 + 2p)) = 0
((-3 * 8 + 2p * 8) + 3p * (-3 + 2p)) = 0
((-24 + 16p) + 3p * (-3 + 2p)) = 0
(-24 + 16p + (-3 * 3p + 2p * 3p)) = 0
(-24 + 16p + (-9p + 6p2)) = 0

Combine like terms: 16p + -9p = 7p
(-24 + 7p + 6p2) = 0

Solving
-24 + 7p + 6p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-8 + -3p)(3 + -2p) = 0

Subproblem 1
Set the factor '(-8 + -3p)' equal to zero and attempt to solve:

Simplifying
-8 + -3p = 0

Solving
-8 + -3p = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3p = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3p = 0 + 8
-3p = 0 + 8

Combine like terms: 0 + 8 = 8
-3p = 8

Divide each side by '-3'.
p = -2.666666667

Simplifying
p = -2.666666667
Subproblem 2
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
Solution
p = {-2.666666667, 1.5}