Solve 49*f(x)=4x-4/2x+3

$$49 \cdot f ( x ) = \frac { 4 x - 4 } { 2 x + 3 }$$

Solve for f

$$f=-\frac{4\left(1-x\right)}{49x\left(2x+3\right)}$$

$$x\neq -\frac{3}{2}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x+3.

$$49fx\left(2x+3\right)=4x-4$$

Use the distributive property to multiply 49fx by 2x+3.

$$98fx^{2}+147fx=4x-4$$

Combine all terms containing f.

$$\left(98x^{2}+147x\right)f=4x-4$$

Divide both sides by 98x^{2}+147x.

$$\frac{\left(98x^{2}+147x\right)f}{98x^{2}+147x}=\frac{4x-4}{98x^{2}+147x}$$

Dividing by 98x^{2}+147x undoes the multiplication by 98x^{2}+147x.

$$f=\frac{4x-4}{98x^{2}+147x}$$

Divide -4+4x by 98x^{2}+147x.

$$f=\frac{4\left(x-1\right)}{49x\left(2x+3\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{21609f^{2}-2744f+16}-147f+4}{196f}\text{; }x=\frac{-\sqrt{21609f^{2}-2744f+16}-147f+4}{196f}\text{, }&f\neq 0\\x=1\text{, }&f=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{21609f^{2}-2744f+16}-147f+4}{196f}\text{; }x=\frac{-\sqrt{21609f^{2}-2744f+16}-147f+4}{196f}\text{, }&\left(f\neq 0\text{ and }f\leq -\frac{8\sqrt{10}}{441}+\frac{4}{63}\right)\text{ or }f\geq \frac{8\sqrt{10}}{441}+\frac{4}{63}\\x=1\text{, }&f=0\end{matrix}\right.$$