(f+g)(x)=(x+1)(x+5)

Solution for (f+g)(x)=(x+1)(x+5) equation:

Simplifying
(f + g)(x) = (x + 1)(x + 5)

Reorder the terms for easier multiplication:
x(f + g) = (x + 1)(x + 5)
(f * x + g * x) = (x + 1)(x + 5)
(fx + gx) = (x + 1)(x + 5)

Reorder the terms:
fx + gx = (1 + x)(x + 5)

Reorder the terms:
fx + gx = (1 + x)(5 + x)

Multiply (1 + x) * (5 + x)
fx + gx = (1(5 + x) + x(5 + x))
fx + gx = ((5 * 1 + x * 1) + x(5 + x))
fx + gx = ((5 + 1x) + x(5 + x))
fx + gx = (5 + 1x + (5 * x + x * x))
fx + gx = (5 + 1x + (5x + x2))

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

Solving
fx + gx = 5 + 6x + x2

Solving for variable 'f'.

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

Add '-1gx' to each side of the equation.
fx + gx + -1gx = 5 + 6x + -1gx + x2

Combine like terms: gx + -1gx = 0
fx + 0 = 5 + 6x + -1gx + x2
fx = 5 + 6x + -1gx + x2

Reorder the terms:
fx = 5 + -1gx + 6x + x2

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

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

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