The problem asks us to solve the equation $4x^2 = 9x$ for $x$.

1. Problem Description

The problem asks us to solve the equation $4x^2 = 9x$ for $x$.

2. Solution Steps

We are given the equation $4x^2 = 9x$. To solve for $x$, we first rearrange the equation to have all terms on one side and zero on the other side:

$4x^2 - 9x = 0$

Now, we can factor out $x$ from the left side:

$x(4x - 9) = 0$

For the product of two factors to be zero, at least one of the factors must be zero. Therefore, we have two possibilities:

$x = 0$ or $4x - 9 = 0$.

If $4x - 9 = 0$, we can add 9 to both sides to get:

$4x = 9$

Then, we divide both sides by 4 to get:

$x = \frac{9}{4}$

Thus, the two solutions are $x = 0$ and $x = \frac{9}{4}$.

3. Final Answer

The solutions to the equation $4x^2 = 9x$ are $x = 0$ and $x = \frac{9}{4}$.