Solve and check the equation. \[ 3(5-2 x)=3(3 x+1) \] Select the correct choice below and, if necessary, fill in any answer box to complete your answer. A. The solution set is B. The solution set is $\{x \mid x$ is a real number $\}$. C. The solution set is $\varnothing$.

Step 1 ：The given equation is a linear equation in one variable, x. To solve it, we need to simplify the equation and isolate x.

Step 2 ：Simplify the equation to get: \(15 - 6x = 9x + 3\)

Step 3 ：Solve the equation to get: \(x = \frac{4}{5}\)

Step 4 ：Check the solution by substituting \(x = \frac{4}{5}\) back into the original equation.

Step 5 ：The solution is correct.

Step 6 ：Final Answer: The solution set is \(\boxed{\left\{x \mid x = \frac{4}{5}\right\}}\)