Solve x/q+x+x*q=35

$$\frac { x } { q } + x + x \cdot q = 35$$

Solve for x (complex solution)

$$x=\frac{35q}{q^{2}+q+1}$$

$$q\neq \frac{-1+\sqrt{3}i}{2}\text{ and }q\neq \frac{-\sqrt{3}i-1}{2}\text{ and }q\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by q.

$$x+qx+xqq=35q$$

Multiply q and q to get q^{2}.

$$x+qx+xq^{2}=35q$$

Combine all terms containing x.

$$\left(1+q+q^{2}\right)x=35q$$

The equation is in standard form.

$$\left(q^{2}+q+1\right)x=35q$$

Divide both sides by q^{2}+q+1.

$$\frac{\left(q^{2}+q+1\right)x}{q^{2}+q+1}=\frac{35q}{q^{2}+q+1}$$

Dividing by q^{2}+q+1 undoes the multiplication by q^{2}+q+1.

$$x=\frac{35q}{q^{2}+q+1}$$

Solve for x

$$x=\frac{35q}{q^{2}+q+1}$$

$$q\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by q.

$$x+qx+xqq=35q$$

Multiply q and q to get q^{2}.

$$x+qx+xq^{2}=35q$$

Combine all terms containing x.

$$\left(1+q+q^{2}\right)x=35q$$

The equation is in standard form.

$$\left(q^{2}+q+1\right)x=35q$$

Divide both sides by q^{2}+q+1.

$$\frac{\left(q^{2}+q+1\right)x}{q^{2}+q+1}=\frac{35q}{q^{2}+q+1}$$

Dividing by q^{2}+q+1 undoes the multiplication by q^{2}+q+1.

$$x=\frac{35q}{q^{2}+q+1}$$

Solve for q (complex solution)

$$q=\frac{\sqrt{-\left(3x-35\right)\left(x+35\right)}-x+35}{2x}$$

$$q=\frac{-\sqrt{-\left(3x-35\right)\left(x+35\right)}-x+35}{2x}\text{, }x\neq 0$$

Solve for q

$$q=\frac{\sqrt{\left(35-3x\right)\left(x+35\right)}-x+35}{2x}$$

$$q=\frac{-\sqrt{\left(35-3x\right)\left(x+35\right)}-x+35}{2x}\text{, }x\neq 0\text{ and }x\geq -35\text{ and }x\leq \frac{35}{3}$$