g(r)=(5r^3+3r+1)(r^2+3)

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Solution for g(r)=(5r^3+3r+1)(r^2+3) equation:


Simplifying
g(r) = (5r3 + 3r + 1)(r2 + 3)

Multiply g * r
gr = (5r3 + 3r + 1)(r2 + 3)

Reorder the terms:
gr = (1 + 3r + 5r3)(r2 + 3)

Reorder the terms:
gr = (1 + 3r + 5r3)(3 + r2)

Multiply (1 + 3r + 5r3) * (3 + r2)
gr = (1(3 + r2) + 3r * (3 + r2) + 5r3 * (3 + r2))
gr = ((3 * 1 + r2 * 1) + 3r * (3 + r2) + 5r3 * (3 + r2))
gr = ((3 + 1r2) + 3r * (3 + r2) + 5r3 * (3 + r2))
gr = (3 + 1r2 + (3 * 3r + r2 * 3r) + 5r3 * (3 + r2))
gr = (3 + 1r2 + (9r + 3r3) + 5r3 * (3 + r2))
gr = (3 + 1r2 + 9r + 3r3 + (3 * 5r3 + r2 * 5r3))
gr = (3 + 1r2 + 9r + 3r3 + (15r3 + 5r5))

Reorder the terms:
gr = (3 + 9r + 1r2 + 3r3 + 15r3 + 5r5)

Combine like terms: 3r3 + 15r3 = 18r3
gr = (3 + 9r + 1r2 + 18r3 + 5r5)

Solving
gr = 3 + 9r + 1r2 + 18r3 + 5r5

Solving for variable 'g'.

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

Divide each side by 'r'.
g = 3r-1 + 9 + r + 18r2 + 5r4

Simplifying
g = 3r-1 + 9 + r + 18r2 + 5r4

Reorder the terms:
g = 9 + 3r-1 + r + 18r2 + 5r4

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