(5n-2)(4n+1)=0

Solution for (5n-2)(4n+1)=0 equation:

Simplifying
(5n + -2)(4n + 1) = 0

Reorder the terms:
(-2 + 5n)(4n + 1) = 0

Reorder the terms:
(-2 + 5n)(1 + 4n) = 0

Multiply (-2 + 5n) * (1 + 4n)
(-2(1 + 4n) + 5n * (1 + 4n)) = 0
((1 * -2 + 4n * -2) + 5n * (1 + 4n)) = 0
((-2 + -8n) + 5n * (1 + 4n)) = 0
(-2 + -8n + (1 * 5n + 4n * 5n)) = 0
(-2 + -8n + (5n + 20n2)) = 0

Combine like terms: -8n + 5n = -3n
(-2 + -3n + 20n2) = 0

Solving
-2 + -3n + 20n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -4n)(2 + -5n) = 0

Subproblem 1
Set the factor '(-1 + -4n)' equal to zero and attempt to solve:

Simplifying
-1 + -4n = 0

Solving
-1 + -4n = 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 + -4n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4n = 0 + 1
-4n = 0 + 1

Combine like terms: 0 + 1 = 1
-4n = 1

Divide each side by '-4'.
n = -0.25

Simplifying
n = -0.25
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 = {-0.25, 0.4}