2l^2+5nl+2n^2=0

Solution for 2l^2+5nl+2n^2=0 equation:

Simplifying
2l2 + 5nl + 2n2 = 0

Reorder the terms:
5ln + 2l2 + 2n2 = 0

Solving
5ln + 2l2 + 2n2 = 0

Solving for variable 'l'.

Factor a trinomial.
(2l + n)(l + 2n) = 0

Subproblem 1
Set the factor '(2l + n)' equal to zero and attempt to solve:

Simplifying
2l + n = 0

Solving
2l + n = 0

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

Add '-1n' to each side of the equation.
2l + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
2l + 0 = 0 + -1n
2l = 0 + -1n
Remove the zero:
2l = -1n

Divide each side by '2'.
l = -0.5n

Simplifying
l = -0.5n
Subproblem 2
Set the factor '(l + 2n)' equal to zero and attempt to solve:

Simplifying
l + 2n = 0

Solving
l + 2n = 0

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

Add '-2n' to each side of the equation.
l + 2n + -2n = 0 + -2n

Combine like terms: 2n + -2n = 0
l + 0 = 0 + -2n
l = 0 + -2n
Remove the zero:
l = -2n

Simplifying
l = -2n
Solution
l = {-0.5n, -2n}