g(3gn)=3gn^2+5(3gn)

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


Simplifying
g(3gn) = 3gn2 + 5(3gn)

Remove parenthesis around (3gn)
g * 3gn = 3gn2 + 5(3gn)

Reorder the terms for easier multiplication:
3g * gn = 3gn2 + 5(3gn)

Multiply g * gn
3g2n = 3gn2 + 5(3gn)

Remove parenthesis around (3gn)
3g2n = 3gn2 + 5 * 3gn

Multiply 5 * 3
3g2n = 3gn2 + 15gn

Reorder the terms:
3g2n = 15gn + 3gn2

Solving
3g2n = 15gn + 3gn2

Solving for variable 'g'.

Reorder the terms:
-15gn + -3gn2 + 3g2n = 15gn + 3gn2 + -15gn + -3gn2

Reorder the terms:
-15gn + -3gn2 + 3g2n = 15gn + -15gn + 3gn2 + -3gn2

Combine like terms: 15gn + -15gn = 0
-15gn + -3gn2 + 3g2n = 0 + 3gn2 + -3gn2
-15gn + -3gn2 + 3g2n = 3gn2 + -3gn2

Combine like terms: 3gn2 + -3gn2 = 0
-15gn + -3gn2 + 3g2n = 0

Factor out the Greatest Common Factor (GCF), '3gn'.
3gn(-5 + -1n + g) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'gn' equal to zero and attempt to solve:

Simplifying
gn = 0

Solving
gn = 0

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

Simplifying
gn = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-5 + -1n + g)' equal to zero and attempt to solve:

Simplifying
-5 + -1n + g = 0

Reorder the terms:
-5 + g + -1n = 0

Solving
-5 + g + -1n = 0

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

Add '5' to each side of the equation.
-5 + g + 5 + -1n = 0 + 5

Reorder the terms:
-5 + 5 + g + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + g + -1n = 0 + 5
g + -1n = 0 + 5

Combine like terms: 0 + 5 = 5
g + -1n = 5

Add 'n' to each side of the equation.
g + -1n + n = 5 + n

Combine like terms: -1n + n = 0
g + 0 = 5 + n
g = 5 + n

Simplifying
g = 5 + n
Solution
g = {5 + n}

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