(5n+4)*(5n-1)=

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

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

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

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

Multiply (4 + 5n) * (-1 + 5n)
(4(-1 + 5n) + 5n * (-1 + 5n)) = 0
((-1 * 4 + 5n * 4) + 5n * (-1 + 5n)) = 0
((-4 + 20n) + 5n * (-1 + 5n)) = 0
(-4 + 20n + (-1 * 5n + 5n * 5n)) = 0
(-4 + 20n + (-5n + 25n2)) = 0

Combine like terms: 20n + -5n = 15n
(-4 + 15n + 25n2) = 0

Solving
-4 + 15n + 25n2 = 0

Solving for variable 'n'.

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

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

Simplifying
1 + -5n = 0

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

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

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

Divide each side by '-5'.
n = 0.2

Simplifying
n = 0.2
Solution
n = {-0.8, 0.2}