(2n-1)(5n+2)=0

Solution for (2n-1)(5n+2)=0 equation:

Simplifying
(2n + -1)(5n + 2) = 0

Reorder the terms:
(-1 + 2n)(5n + 2) = 0

Reorder the terms:
(-1 + 2n)(2 + 5n) = 0

Multiply (-1 + 2n) * (2 + 5n)
(-1(2 + 5n) + 2n * (2 + 5n)) = 0
((2 * -1 + 5n * -1) + 2n * (2 + 5n)) = 0
((-2 + -5n) + 2n * (2 + 5n)) = 0
(-2 + -5n + (2 * 2n + 5n * 2n)) = 0
(-2 + -5n + (4n + 10n2)) = 0

Combine like terms: -5n + 4n = -1n
(-2 + -1n + 10n2) = 0

Solving
-2 + -1n + 10n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-2 + -5n)(1 + -2n) = 0

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

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

Simplifying
n = 0.5
Solution
n = {-0.4, 0.5}