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

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

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

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

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

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

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

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

Solving for variable 'n'.

Factor a trinomial.
(-5 + -2n)(4 + -1n) = 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 '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

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

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

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-2.5, 4}