4n=4n(n-1)d

Solution for 4n=4n(n-1)d equation:

Simplifying
4n = 4n(n + -1) * d

Reorder the terms:
4n = 4n(-1 + n) * d

Reorder the terms for easier multiplication:
4n = 4n * d(-1 + n)

Multiply n * d
4n = 4dn(-1 + n)
4n = (-1 * 4dn + n * 4dn)
4n = (-4dn + 4dn2)

Solving
4n = -4dn + 4dn2

Solving for variable 'n'.

Reorder the terms:
4dn + -4dn2 + 4n = -4dn + 4dn2 + 4dn + -4dn2

Reorder the terms:
4dn + -4dn2 + 4n = -4dn + 4dn + 4dn2 + -4dn2

Combine like terms: -4dn + 4dn = 0
4dn + -4dn2 + 4n = 0 + 4dn2 + -4dn2
4dn + -4dn2 + 4n = 4dn2 + -4dn2

Combine like terms: 4dn2 + -4dn2 = 0
4dn + -4dn2 + 4n = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(d + -1dn + 1)' equal to zero and attempt to solve:

Simplifying
d + -1dn + 1 = 0

Reorder the terms:
1 + d + -1dn = 0

Solving
1 + d + -1dn = 0

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

Add '-1' to each side of the equation.
1 + d + -1 + -1dn = 0 + -1

Reorder the terms:
1 + -1 + d + -1dn = 0 + -1

Combine like terms: 1 + -1 = 0
0 + d + -1dn = 0 + -1
d + -1dn = 0 + -1

Combine like terms: 0 + -1 = -1
d + -1dn = -1

Add '-1d' to each side of the equation.
d + -1d + -1dn = -1 + -1d

Combine like terms: d + -1d = 0
0 + -1dn = -1 + -1d
-1dn = -1 + -1d

Divide each side by '-1d'.
n = d-1 + 1

Simplifying
n = d-1 + 1

Reorder the terms:
n = 1 + d-1
Solution
n = {0, 1 + d-1}