h(n)=2(n+4)(n+4)(n+4)-(n+4)(n+4)

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Solution for h(n)=2(n+4)(n+4)(n+4)-(n+4)(n+4) equation: 


Simplifying
h(n) = 2(n + 4)(n + 4)(n + 4) + -1(n + 4)(n + 4)

Multiply h * n
hn = 2(n + 4)(n + 4)(n + 4) + -1(n + 4)(n + 4)

Reorder the terms:
hn = 2(4 + n)(n + 4)(n + 4) + -1(n + 4)(n + 4)

Reorder the terms:
hn = 2(4 + n)(4 + n)(n + 4) + -1(n + 4)(n + 4)

Reorder the terms:
hn = 2(4 + n)(4 + n)(4 + n) + -1(n + 4)(n + 4)

Multiply (4 + n) * (4 + n)
hn = 2(4(4 + n) + n(4 + n))(4 + n) + -1(n + 4)(n + 4)
hn = 2((4 * 4 + n * 4) + n(4 + n))(4 + n) + -1(n + 4)(n + 4)
hn = 2((16 + 4n) + n(4 + n))(4 + n) + -1(n + 4)(n + 4)
hn = 2(16 + 4n + (4 * n + n * n))(4 + n) + -1(n + 4)(n + 4)
hn = 2(16 + 4n + (4n + n2))(4 + n) + -1(n + 4)(n + 4)

Combine like terms: 4n + 4n = 8n
hn = 2(16 + 8n + n2)(4 + n) + -1(n + 4)(n + 4)

Multiply (16 + 8n + n2) * (4 + n)
hn = 2(16(4 + n) + 8n * (4 + n) + n2(4 + n)) + -1(n + 4)(n + 4)
hn = 2((4 * 16 + n * 16) + 8n * (4 + n) + n2(4 + n)) + -1(n + 4)(n + 4)
hn = 2((64 + 16n) + 8n * (4 + n) + n2(4 + n)) + -1(n + 4)(n + 4)
hn = 2(64 + 16n + (4 * 8n + n * 8n) + n2(4 + n)) + -1(n + 4)(n + 4)
hn = 2(64 + 16n + (32n + 8n2) + n2(4 + n)) + -1(n + 4)(n + 4)
hn = 2(64 + 16n + 32n + 8n2 + (4 * n2 + n * n2)) + -1(n + 4)(n + 4)
hn = 2(64 + 16n + 32n + 8n2 + (4n2 + n3)) + -1(n + 4)(n + 4)

Combine like terms: 16n + 32n = 48n
hn = 2(64 + 48n + 8n2 + 4n2 + n3) + -1(n + 4)(n + 4)

Combine like terms: 8n2 + 4n2 = 12n2
hn = 2(64 + 48n + 12n2 + n3) + -1(n + 4)(n + 4)
hn = (64 * 2 + 48n * 2 + 12n2 * 2 + n3 * 2) + -1(n + 4)(n + 4)
hn = (128 + 96n + 24n2 + 2n3) + -1(n + 4)(n + 4)

Reorder the terms:
hn = 128 + 96n + 24n2 + 2n3 + -1(4 + n)(n + 4)

Reorder the terms:
hn = 128 + 96n + 24n2 + 2n3 + -1(4 + n)(4 + n)

Multiply (4 + n) * (4 + n)
hn = 128 + 96n + 24n2 + 2n3 + -1(4(4 + n) + n(4 + n))
hn = 128 + 96n + 24n2 + 2n3 + -1((4 * 4 + n * 4) + n(4 + n))
hn = 128 + 96n + 24n2 + 2n3 + -1((16 + 4n) + n(4 + n))
hn = 128 + 96n + 24n2 + 2n3 + -1(16 + 4n + (4 * n + n * n))
hn = 128 + 96n + 24n2 + 2n3 + -1(16 + 4n + (4n + n2))

Combine like terms: 4n + 4n = 8n
hn = 128 + 96n + 24n2 + 2n3 + -1(16 + 8n + n2)
hn = 128 + 96n + 24n2 + 2n3 + (16 * -1 + 8n * -1 + n2 * -1)
hn = 128 + 96n + 24n2 + 2n3 + (-16 + -8n + -1n2)

Reorder the terms:
hn = 128 + -16 + 96n + -8n + 24n2 + -1n2 + 2n3

Combine like terms: 128 + -16 = 112
hn = 112 + 96n + -8n + 24n2 + -1n2 + 2n3

Combine like terms: 96n + -8n = 88n
hn = 112 + 88n + 24n2 + -1n2 + 2n3

Combine like terms: 24n2 + -1n2 = 23n2
hn = 112 + 88n + 23n2 + 2n3

Solving
hn = 112 + 88n + 23n2 + 2n3

Solving for variable 'h'.

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

Divide each side by 'n'.
h = 112n-1 + 88 + 23n + 2n2

Simplifying
h = 112n-1 + 88 + 23n + 2n2

Reorder the terms:
h = 88 + 112n-1 + 23n + 2n2

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