(fg)(x)=(x+1)(x+5)

Solution for (fg)(x)=(x+1)(x+5) equation:

Simplifying
(fg)(x) = (x + 1)(x + 5)

Multiply fg * x
fgx = (x + 1)(x + 5)

Reorder the terms:
fgx = (1 + x)(x + 5)

Reorder the terms:
fgx = (1 + x)(5 + x)

Multiply (1 + x) * (5 + x)
fgx = (1(5 + x) + x(5 + x))
fgx = ((5 * 1 + x * 1) + x(5 + x))
fgx = ((5 + 1x) + x(5 + x))
fgx = (5 + 1x + (5 * x + x * x))
fgx = (5 + 1x + (5x + x2))

Combine like terms: 1x + 5x = 6x
fgx = (5 + 6x + x2)

Solving
fgx = 5 + 6x + x2

Solving for variable 'f'.

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

Divide each side by 'gx'.
f = 5g-1x-1 + 6g-1 + g-1x

Simplifying
f = 5g-1x-1 + 6g-1 + g-1x

Reorder the terms:
f = 6g-1 + 5g-1x-1 + g-1x