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

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

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

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

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

Multiply (-4 + 5n) * (5 + n)
(-4(5 + n) + 5n * (5 + n)) = 0
((5 * -4 + n * -4) + 5n * (5 + n)) = 0
((-20 + -4n) + 5n * (5 + n)) = 0
(-20 + -4n + (5 * 5n + n * 5n)) = 0
(-20 + -4n + (25n + 5n2)) = 0

Combine like terms: -4n + 25n = 21n
(-20 + 21n + 5n2) = 0

Solving
-20 + 21n + 5n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 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 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(4 + -5n)' equal to zero and attempt to solve:

Simplifying
4 + -5n = 0

Solving
4 + -5n = 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 + -5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5n = 0 + -4
-5n = 0 + -4

Combine like terms: 0 + -4 = -4
-5n = -4

Divide each side by '-5'.
n = 0.8

Simplifying
n = 0.8
Solution
n = {-5, 0.8}