Solve f(x)+3f(1-x)=2x^2+x-7

$$f ( x ) + 3 f ( 1 - x ) = 2 x ^ { 2 } + x - 7$$

Solve for f

$$f=-\frac{7-x-2x^{2}}{3-2x}$$

$$x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3f by 1-x.

$$fx+3f-3fx=2x^{2}+x-7$$

Combine fx and -3fx to get -2fx.

$$-2fx+3f=2x^{2}+x-7$$

Combine all terms containing f.

$$\left(-2x+3\right)f=2x^{2}+x-7$$

The equation is in standard form.

$$\left(3-2x\right)f=2x^{2}+x-7$$

Divide both sides by -2x+3.

$$\frac{\left(3-2x\right)f}{3-2x}=\frac{2x^{2}+x-7}{3-2x}$$

Dividing by -2x+3 undoes the multiplication by -2x+3.

$$f=\frac{2x^{2}+x-7}{3-2x}$$

Solve for x

$$x=-\frac{\sqrt{4f^{2}+28f+57}}{4}-\frac{f}{2}-\frac{1}{4}$$

$$x=\frac{\sqrt{4f^{2}+28f+57}}{4}-\frac{f}{2}-\frac{1}{4}$$