(3p+2)x(2p+1)=0

Solution for (3p+2)x(2p+1)=0 equation:

Simplifying
(3p + 2) * x(2p + 1) = 0

Reorder the terms:
(2 + 3p) * x(2p + 1) = 0

Reorder the terms:
(2 + 3p) * x(1 + 2p) = 0

Reorder the terms for easier multiplication:
x(2 + 3p)(1 + 2p) = 0

Multiply (2 + 3p) * (1 + 2p)
x(2(1 + 2p) + 3p * (1 + 2p)) = 0
x((1 * 2 + 2p * 2) + 3p * (1 + 2p)) = 0
x((2 + 4p) + 3p * (1 + 2p)) = 0
x(2 + 4p + (1 * 3p + 2p * 3p)) = 0
x(2 + 4p + (3p + 6p2)) = 0

Combine like terms: 4p + 3p = 7p
x(2 + 7p + 6p2) = 0
(2 * x + 7p * x + 6p2 * x) = 0

Reorder the terms:
(7px + 6p2x + 2x) = 0
(7px + 6p2x + 2x) = 0

Solving
7px + 6p2x + 2x = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7p + 6p2 + 2) = 0

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2p + 1)' equal to zero and attempt to solve:

Simplifying
2p + 1 = 0

Reorder the terms:
1 + 2p = 0

Solving
1 + 2p = 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 + 2p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2p = 0 + -1
2p = 0 + -1

Combine like terms: 0 + -1 = -1
2p = -1

Divide each side by '2'.
p = -0.5

Simplifying
p = -0.5
Subproblem 3
Set the factor '(3p + 2)' equal to zero and attempt to solve:

Simplifying
3p + 2 = 0

Reorder the terms:
2 + 3p = 0

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

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

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

Divide each side by '3'.
p = -0.6666666667

Simplifying
p = -0.6666666667
Solution
p = {-0.5, -0.6666666667}