(f-g)(x)=(f(x^2-9))-(2x)

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Solution for (f-g)(x)=(f(x^2-9))-(2x) equation: 


Simplifying
(f + -1g)(x) = (f(x2 + -9)) + -1(2x)

Reorder the terms for easier multiplication:
x(f + -1g) = (f(x2 + -9)) + -1(2x)
(f * x + -1g * x) = (f(x2 + -9)) + -1(2x)
(fx + -1gx) = (f(x2 + -9)) + -1(2x)

Reorder the terms:
fx + -1gx = (f(-9 + x2)) + -1(2x)
fx + -1gx = ((-9 * f + x2 * f)) + -1(2x)
fx + -1gx = ((-9f + fx2)) + -1(2x)
fx + -1gx = (-9f + fx2) + -1(2x)

Remove parenthesis around (-9f + fx2)
fx + -1gx = -9f + fx2 + -1(2x)

Remove parenthesis around (2x)
fx + -1gx = -9f + fx2 + -1 * 2x

Multiply -1 * 2
fx + -1gx = -9f + fx2 + -2x

Solving
fx + -1gx = -9f + fx2 + -2x

Solving for variable 'f'.

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

Add '9f' to each side of the equation.
fx + 9f + -1gx = -9f + fx2 + 9f + -2x

Reorder the terms:
9f + fx + -1gx = -9f + fx2 + 9f + -2x

Reorder the terms:
9f + fx + -1gx = -9f + 9f + fx2 + -2x

Combine like terms: -9f + 9f = 0
9f + fx + -1gx = 0 + fx2 + -2x
9f + fx + -1gx = fx2 + -2x

Add '-1fx2' to each side of the equation.
9f + fx + -1fx2 + -1gx = fx2 + -1fx2 + -2x

Combine like terms: fx2 + -1fx2 = 0
9f + fx + -1fx2 + -1gx = 0 + -2x
9f + fx + -1fx2 + -1gx = -2x

Add 'gx' to each side of the equation.
9f + fx + -1fx2 + -1gx + gx = gx + -2x

Combine like terms: -1gx + gx = 0
9f + fx + -1fx2 + 0 = gx + -2x
9f + fx + -1fx2 = gx + -2x

Reorder the terms:
9f + fx + -1fx2 + -1gx + 2x = gx + -1gx + -2x + 2x

Combine like terms: gx + -1gx = 0
9f + fx + -1fx2 + -1gx + 2x = 0 + -2x + 2x
9f + fx + -1fx2 + -1gx + 2x = -2x + 2x

Combine like terms: -2x + 2x = 0
9f + fx + -1fx2 + -1gx + 2x = 0

The solution to this equation could not be determined.

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