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

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

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

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

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

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

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

Solving
0 = 4 + 25n + 25n2

Solving for variable 'n'.

Combine like terms: 0 + -4 = -4
-4 + -25n + -25n2 = 4 + 25n + 25n2 + -4 + -25n + -25n2

Reorder the terms:
-4 + -25n + -25n2 = 4 + -4 + 25n + -25n + 25n2 + -25n2

Combine like terms: 4 + -4 = 0
-4 + -25n + -25n2 = 0 + 25n + -25n + 25n2 + -25n2
-4 + -25n + -25n2 = 25n + -25n + 25n2 + -25n2

Combine like terms: 25n + -25n = 0
-4 + -25n + -25n2 = 0 + 25n2 + -25n2
-4 + -25n + -25n2 = 25n2 + -25n2

Combine like terms: 25n2 + -25n2 = 0
-4 + -25n + -25n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 25n + 25n2) = 0

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

Ignore the factor -1.
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}