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

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

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

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

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

Multiply (1 + 5p) * (5 + p)
(1(5 + p) + 5p * (5 + p)) = 0
((5 * 1 + p * 1) + 5p * (5 + p)) = 0
((5 + 1p) + 5p * (5 + p)) = 0
(5 + 1p + (5 * 5p + p * 5p)) = 0
(5 + 1p + (25p + 5p2)) = 0

Combine like terms: 1p + 25p = 26p
(5 + 26p + 5p2) = 0

Solving
5 + 26p + 5p2 = 0

Solving for variable 'p'.

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

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

Simplifying
5 + p = 0

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

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

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

Simplifying
p = -5
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 = {-5, -0.2}