Solve f(3x+5)(3x-5)=(9x-5)*(x-5)17

$$f ( 3 x + 5 ) ( 3 x - 5 ) = ( 9 x - 5 ) \cdot ( x - 5 ) 17$$

Solve for f (complex solution)

$$f=-\frac{17\left(5-x\right)\left(9x-5\right)}{9x^{2}-25}$$

$$x\neq -\frac{5}{3}\text{ and }x\neq \frac{5}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by 3x+5.

$$\left(3fx+5f\right)\left(3x-5\right)=\left(9x-5\right)\left(x-5\right)\times 17$$

Use the distributive property to multiply 3fx+5f by 3x-5 and combine like terms.

$$9fx^{2}-25f=\left(9x-5\right)\left(x-5\right)\times 17$$

Use the distributive property to multiply 9x-5 by x-5 and combine like terms.

$$9fx^{2}-25f=\left(9x^{2}-50x+25\right)\times 17$$

Use the distributive property to multiply 9x^{2}-50x+25 by 17.

$$9fx^{2}-25f=153x^{2}-850x+425$$

Combine all terms containing f.

$$\left(9x^{2}-25\right)f=153x^{2}-850x+425$$

Divide both sides by 9x^{2}-25.

$$\frac{\left(9x^{2}-25\right)f}{9x^{2}-25}=\frac{17\left(x-5\right)\left(9x-5\right)}{9x^{2}-25}$$

Dividing by 9x^{2}-25 undoes the multiplication by 9x^{2}-25.

$$f=\frac{17\left(x-5\right)\left(9x-5\right)}{9x^{2}-25}$$

Solve for f

$$f=-\frac{17\left(5-x\right)\left(9x-5\right)}{9x^{2}-25}$$

$$|x|\neq \frac{5}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by 3x+5.

$$\left(3fx+5f\right)\left(3x-5\right)=\left(9x-5\right)\left(x-5\right)\times 17$$

Use the distributive property to multiply 3fx+5f by 3x-5 and combine like terms.

$$9fx^{2}-25f=\left(9x-5\right)\left(x-5\right)\times 17$$

Use the distributive property to multiply 9x-5 by x-5 and combine like terms.

$$9fx^{2}-25f=\left(9x^{2}-50x+25\right)\times 17$$

Use the distributive property to multiply 9x^{2}-50x+25 by 17.

$$9fx^{2}-25f=153x^{2}-850x+425$$

Combine all terms containing f.

$$\left(9x^{2}-25\right)f=153x^{2}-850x+425$$

Divide both sides by 9x^{2}-25.

$$\frac{\left(9x^{2}-25\right)f}{9x^{2}-25}=\frac{17\left(x-5\right)\left(9x-5\right)}{9x^{2}-25}$$

Dividing by 9x^{2}-25 undoes the multiplication by 9x^{2}-25.

$$f=\frac{17\left(x-5\right)\left(9x-5\right)}{9x^{2}-25}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{5\left(\sqrt{9f^{2}+4624}-85\right)}{9\left(f-17\right)}\text{; }x=-\frac{5\left(\sqrt{9f^{2}+4624}+85\right)}{9\left(f-17\right)}\text{, }&f\neq 17\\x=1\text{, }&f=17\end{matrix}\right.$$