5p^2+54p+40=0

Solution for 5p^2+54p+40=0 equation:

Simplifying
5p2 + 54p + 40 = 0

Reorder the terms:
40 + 54p + 5p2 = 0

Solving
40 + 54p + 5p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(10 + p)(4 + 5p) = 0

Subproblem 1
Set the factor '(10 + p)' equal to zero and attempt to solve:

Simplifying
10 + p = 0

Solving
10 + p = 0

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

Add '-10' to each side of the equation.
10 + -10 + p = 0 + -10

Combine like terms: 10 + -10 = 0
0 + p = 0 + -10
p = 0 + -10

Combine like terms: 0 + -10 = -10
p = -10

Simplifying
p = -10
Subproblem 2
Set the factor '(4 + 5p)' equal to zero and attempt to solve:

Simplifying
4 + 5p = 0

Solving
4 + 5p = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5p = 0 + -4
5p = 0 + -4

Combine like terms: 0 + -4 = -4
5p = -4

Divide each side by '5'.
p = -0.8

Simplifying
p = -0.8
Solution
p = {-10, -0.8}