5p^2+26p+5=0

Solution for 5p^2+26p+5=0 equation:

Simplifying
5p2 + 26p + 5 = 0

Reorder the terms:
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}