Solve the equation. \[ \frac{2 x-6}{x}=\frac{x-3}{3} \]

Solve the equation \( \frac{2x-6}{x}=\frac{x-3}{3} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{2x-6}{x}=\frac{x-3}{3}\) - step1: Find the domain: \(\frac{2x-6}{x}=\frac{x-3}{3},x\neq 0\) - step2: Cross multiply: \(\left(2x-6\right)\times 3=x\left(x-3\right)\) - step3: Simplify the equation: \(3\left(2x-6\right)=x\left(x-3\right)\) - step4: Calculate: \(6x-18=x\left(x-3\right)\) - step5: Calculate: \(6x-18=x^{2}-3x\) - step6: Move the expression to the left side: \(6x-18-\left(x^{2}-3x\right)=0\) - step7: Calculate: \(9x-18-x^{2}=0\) - step8: Factor the expression: \(\left(-6+x\right)\left(3-x\right)=0\) - step9: Separate into possible cases: \(\begin{align}&-6+x=0\\&3-x=0\end{align}\) - step10: Solve the equation: \(\begin{align}&x=6\\&x=3\end{align}\) - step11: Check if the solution is in the defined range: \(\begin{align}&x=6\\&x=3\end{align},x\neq 0\) - step12: Find the intersection: \(\begin{align}&x=6\\&x=3\end{align}\) - step13: Rewrite: \(x_{1}=3,x_{2}=6\) The solutions to the equation \(\frac{2x-6}{x}=\frac{x-3}{3}\) are \(x=3\) and \(x=6\).