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

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

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

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

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

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

Multiply (3 + 2p) * (1 + 3p)
x(3(1 + 3p) + 2p * (1 + 3p)) = 0
x((1 * 3 + 3p * 3) + 2p * (1 + 3p)) = 0
x((3 + 9p) + 2p * (1 + 3p)) = 0
x(3 + 9p + (1 * 2p + 3p * 2p)) = 0
x(3 + 9p + (2p + 6p2)) = 0

Combine like terms: 9p + 2p = 11p
x(3 + 11p + 6p2) = 0
(3 * x + 11p * x + 6p2 * x) = 0

Reorder the terms:
(11px + 6p2x + 3x) = 0
(11px + 6p2x + 3x) = 0

Solving
11px + 6p2x + 3x = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(11p + 6p2 + 3) = 0

Factor a trinomial.
x((3p + 1)(2p + 3)) = 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 '(3p + 1)' equal to zero and attempt to solve:

Simplifying
3p + 1 = 0

Reorder the terms:
1 + 3p = 0

Solving
1 + 3p = 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 + 3p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3p = 0 + -1
3p = 0 + -1

Combine like terms: 0 + -1 = -1
3p = -1

Divide each side by '3'.
p = -0.3333333333

Simplifying
p = -0.3333333333
Subproblem 3
Set the factor '(2p + 3)' equal to zero and attempt to solve:

Simplifying
2p + 3 = 0

Reorder the terms:
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 = {-0.3333333333, -1.5}