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

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

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

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

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

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

Combine like terms: 15p + -1p = 14p
(-5 + 14p + 3p2) = 0

Solving
-5 + 14p + 3p2 = 0

Solving for variable 'p'.

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

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

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1p = 0 + 5

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

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

Divide each side by '-1'.
p = -5

Simplifying
p = -5
Subproblem 2
Set the factor '(1 + -3p)' equal to zero and attempt to solve:

Simplifying
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
Solution
p = {-5, 0.3333333333}