n=n(2n-1)h

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Solution for n=n(2n-1)h equation: 


Simplifying
n = n(2n + -1) * h

Reorder the terms:
n = n(-1 + 2n) * h

Reorder the terms for easier multiplication:
n = n * h(-1 + 2n)

Multiply n * h
n = hn(-1 + 2n)
n = (-1 * hn + 2n * hn)
n = (-1hn + 2hn2)

Solving
n = -1hn + 2hn2

Solving for variable 'n'.

Reorder the terms:
hn + -2hn2 + n = -1hn + 2hn2 + hn + -2hn2

Reorder the terms:
hn + -2hn2 + n = -1hn + hn + 2hn2 + -2hn2

Combine like terms: -1hn + hn = 0
hn + -2hn2 + n = 0 + 2hn2 + -2hn2
hn + -2hn2 + n = 2hn2 + -2hn2

Combine like terms: 2hn2 + -2hn2 = 0
hn + -2hn2 + n = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(h + -2hn + 1) = 0


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 '(h + -2hn + 1)' equal to zero and attempt to solve:

Simplifying
h + -2hn + 1 = 0

Reorder the terms:
1 + h + -2hn = 0

Solving
1 + h + -2hn = 0

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

Add '-1' to each side of the equation.
1 + h + -1 + -2hn = 0 + -1

Reorder the terms:
1 + -1 + h + -2hn = 0 + -1

Combine like terms: 1 + -1 = 0
0 + h + -2hn = 0 + -1
h + -2hn = 0 + -1

Combine like terms: 0 + -1 = -1
h + -2hn = -1

Add '-1h' to each side of the equation.
h + -1h + -2hn = -1 + -1h

Combine like terms: h + -1h = 0
0 + -2hn = -1 + -1h
-2hn = -1 + -1h

Divide each side by '-2h'.
n = 0.5h-1 + 0.5

Simplifying
n = 0.5h-1 + 0.5

Reorder the terms:
n = 0.5 + 0.5h-1
Solution
n = {0, 0.5 + 0.5h-1}

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