(f*g)(x)=(4x+1)*(x^2-5)

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Solution for (f*g)(x)=(4x+1)*(x^2-5) equation: 


Simplifying
(f * g)(x) = (4x + 1)(x2 + -5)

Multiply f * g
(fg)(x) = (4x + 1)(x2 + -5)

Multiply fg * x
fgx = (4x + 1)(x2 + -5)

Reorder the terms:
fgx = (1 + 4x)(x2 + -5)

Reorder the terms:
fgx = (1 + 4x)(-5 + x2)

Multiply (1 + 4x) * (-5 + x2)
fgx = (1(-5 + x2) + 4x * (-5 + x2))
fgx = ((-5 * 1 + x2 * 1) + 4x * (-5 + x2))
fgx = ((-5 + 1x2) + 4x * (-5 + x2))
fgx = (-5 + 1x2 + (-5 * 4x + x2 * 4x))
fgx = (-5 + 1x2 + (-20x + 4x3))

Reorder the terms:
fgx = (-5 + -20x + 1x2 + 4x3)
fgx = (-5 + -20x + 1x2 + 4x3)

Solving
fgx = -5 + -20x + 1x2 + 4x3

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 + -20g-1 + g-1x + 4g-1x2

Simplifying
f = -5g-1x-1 + -20g-1 + g-1x + 4g-1x2

Reorder the terms:
f = -20g-1 + -5g-1x-1 + g-1x + 4g-1x2

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