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

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

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

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

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

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

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

Solving
-5 + -14p + 3p2 = 0

Solving for variable 'p'.

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

Subproblem 1
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
Subproblem 2
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
Solution
p = {-0.3333333333, 5}