(5p+1)(3p+2)=0

Solution for (5p+1)(3p+2)=0 equation:

Simplifying
(5p + 1)(3p + 2) = 0

Reorder the terms:
(1 + 5p)(3p + 2) = 0

Reorder the terms:
(1 + 5p)(2 + 3p) = 0

Multiply (1 + 5p) * (2 + 3p)
(1(2 + 3p) + 5p * (2 + 3p)) = 0
((2 * 1 + 3p * 1) + 5p * (2 + 3p)) = 0
((2 + 3p) + 5p * (2 + 3p)) = 0
(2 + 3p + (2 * 5p + 3p * 5p)) = 0
(2 + 3p + (10p + 15p2)) = 0

Combine like terms: 3p + 10p = 13p
(2 + 13p + 15p2) = 0

Solving
2 + 13p + 15p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(2 + 3p)(1 + 5p) = 0

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

Simplifying
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
Subproblem 2
Set the factor '(1 + 5p)' equal to zero and attempt to solve:

Simplifying
1 + 5p = 0

Solving
1 + 5p = 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 + 5p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5p = 0 + -1
5p = 0 + -1

Combine like terms: 0 + -1 = -1
5p = -1

Divide each side by '5'.
p = -0.2

Simplifying
p = -0.2
Solution
p = {-0.6666666667, -0.2}