f(x)=5x^2+7x-5(f+g)(x)

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Solution for f(x)=5x^2+7x-5(f+g)(x) equation:


Simplifying
f(x) = 5x2 + 7x + -5(f + g)(x)

Multiply f * x
fx = 5x2 + 7x + -5(f + g)(x)

Reorder the terms for easier multiplication:
fx = 5x2 + 7x + -5x(f + g)
fx = 5x2 + 7x + (f * -5x + g * -5x)
fx = 5x2 + 7x + (-5fx + -5gx)

Reorder the terms:
fx = -5fx + -5gx + 7x + 5x2

Solving
fx = -5fx + -5gx + 7x + 5x2

Solving for variable 'f'.

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

Add '5fx' to each side of the equation.
fx + 5fx = -5fx + -5gx + 7x + 5fx + 5x2

Combine like terms: fx + 5fx = 6fx
6fx = -5fx + -5gx + 7x + 5fx + 5x2

Reorder the terms:
6fx = -5fx + 5fx + -5gx + 7x + 5x2

Combine like terms: -5fx + 5fx = 0
6fx = 0 + -5gx + 7x + 5x2
6fx = -5gx + 7x + 5x2

Divide each side by '6x'.
f = -0.8333333333g + 1.166666667 + 0.8333333333x

Simplifying
f = -0.8333333333g + 1.166666667 + 0.8333333333x

Reorder the terms:
f = 1.166666667 + -0.8333333333g + 0.8333333333x

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