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

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

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

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

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

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

Combine like terms: 15p + 1p = 16p
(3 + 16p + 5p2) = 0

Solving
3 + 16p + 5p2 = 0

Solving for variable 'p'.

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

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

Simplifying
3 + p = 0

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

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

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

Simplifying
p = -3
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 = {-3, -0.2}