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

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

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

Reorder the terms:
(-2 + 5n)(2n + 5) = 0

Reorder the terms:
(-2 + 5n)(5 + 2n) = 0

Multiply (-2 + 5n) * (5 + 2n)
(-2(5 + 2n) + 5n * (5 + 2n)) = 0
((5 * -2 + 2n * -2) + 5n * (5 + 2n)) = 0
((-10 + -4n) + 5n * (5 + 2n)) = 0
(-10 + -4n + (5 * 5n + 2n * 5n)) = 0
(-10 + -4n + (25n + 10n2)) = 0

Combine like terms: -4n + 25n = 21n
(-10 + 21n + 10n2) = 0

Solving
-10 + 21n + 10n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -2n)(2 + -5n) = 0

Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve:

Simplifying
-5 + -2n = 0

Solving
-5 + -2n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2n = 0 + 5
-2n = 0 + 5

Combine like terms: 0 + 5 = 5
-2n = 5

Divide each side by '-2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 2
Set the factor '(2 + -5n)' equal to zero and attempt to solve:

Simplifying
2 + -5n = 0

Solving
2 + -5n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5n = 0 + -2
-5n = 0 + -2

Combine like terms: 0 + -2 = -2
-5n = -2

Divide each side by '-5'.
n = 0.4

Simplifying
n = 0.4
Solution
n = {-2.5, 0.4}