Let's solve the given equation for [tex]\(G\)[/tex]:
[tex]\[ N^3 - 5hG = 3G \][/tex]
Step 1: Combine like terms involving [tex]\(G\)[/tex] on one side of the equation.
[tex]\[ N^3 = 3G + 5hG \][/tex]
Step 2: Factor [tex]\(G\)[/tex] out from the terms on the right-hand side.
[tex]\[ N^3 = G(3 + 5h) \][/tex]
Step 3: Isolate [tex]\(G\)[/tex] by dividing both sides of the equation by [tex]\(3 + 5h\)[/tex].
[tex]\[ G = \frac{N^3}{3 + 5h} \][/tex]
So, the solution to the equation [tex]\( N^3 - 5hG = 3G \)[/tex] for [tex]\(G\)[/tex] is:
[tex]\[ G = \frac{N^3}{3 + 5h} \][/tex]
