n(2n-5n)+5(n^2-2)=0

Solution for n(2n-5n)+5(n^2-2)=0 equation:

Simplifying
n(2n + -5n) + 5(n2 + -2) = 0

Combine like terms: 2n + -5n = -3n
n(-3n) + 5(n2 + -2) = 0

Remove parenthesis around (-3n)
n * -3n + 5(n2 + -2) = 0

Reorder the terms for easier multiplication:
-3n * n + 5(n2 + -2) = 0

Multiply n * n
-3n2 + 5(n2 + -2) = 0

Reorder the terms:
-3n2 + 5(-2 + n2) = 0
-3n2 + (-2 * 5 + n2 * 5) = 0
-3n2 + (-10 + 5n2) = 0

Reorder the terms:
-10 + -3n2 + 5n2 = 0

Combine like terms: -3n2 + 5n2 = 2n2
-10 + 2n2 = 0

Solving
-10 + 2n2 = 0

Solving for variable 'n'.

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

Add '10' to each side of the equation.
-10 + 10 + 2n2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2n2 = 0 + 10
2n2 = 0 + 10

Combine like terms: 0 + 10 = 10
2n2 = 10

Divide each side by '2'.
n2 = 5

Simplifying
n2 = 5

Take the square root of each side:
n = {-2.236067978, 2.236067978}