Solve f(1000(1+x)-500](1+x)=660

$$f ( 1000 ( 1 + x ) - 500 ] ( 1 + x ) = 660$$

Solve for f

$$f=\frac{33}{25\left(x+1\right)\left(2x+1\right)}$$

$$x\neq -\frac{1}{2}\text{ and }x\neq -1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1000 by 1+x.

$$f\left(1000+1000x-500\right)\left(1+x\right)=660$$

Subtract 500 from 1000 to get 500.

$$f\left(500+1000x\right)\left(1+x\right)=660$$

Use the distributive property to multiply f by 500+1000x.

$$\left(500f+1000fx\right)\left(1+x\right)=660$$

Use the distributive property to multiply 500f+1000fx by 1+x and combine like terms.

$$500f+1500fx+1000fx^{2}=660$$

Combine all terms containing f.

$$\left(500+1500x+1000x^{2}\right)f=660$$

The equation is in standard form.

$$\left(1000x^{2}+1500x+500\right)f=660$$

Divide both sides by 500+1500x+1000x^{2}.

$$\frac{\left(1000x^{2}+1500x+500\right)f}{1000x^{2}+1500x+500}=\frac{660}{1000x^{2}+1500x+500}$$

Dividing by 500+1500x+1000x^{2} undoes the multiplication by 500+1500x+1000x^{2}.

$$f=\frac{660}{1000x^{2}+1500x+500}$$

Divide 660 by 500+1500x+1000x^{2}.

$$f=\frac{33}{25\left(x+1\right)\left(2x+1\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{25f^{2}+264f}}{20f}-\frac{3}{4}$$

$$x=-\frac{\sqrt{25f^{2}+264f}}{20f}-\frac{3}{4}\text{, }f\neq 0$$

Solve for x

$$x=\frac{\sqrt{25f^{2}+264f}}{20f}-\frac{3}{4}$$

$$x=-\frac{\sqrt{25f^{2}+264f}}{20f}-\frac{3}{4}\text{, }f>0\text{ or }f\leq -\frac{264}{25}$$