We are asked to solve the equation $4x^2 = 9x$.

1. Problem Description

We are asked to solve the equation $4x^2 = 9x$.

2. Solution Steps

First, we move all terms to one side of the equation:

$4x^2 - 9x = 0$

Next, we factor out the common factor $x$:

$x(4x - 9) = 0$

Now, we have a product of two terms that equals zero. This means that either the first term is zero or the second term is zero. Thus we have two cases:

Case 1: $x = 0$

Case 2: $4x - 9 = 0$

Add 9 to both sides: $4x = 9$

Divide both sides by 4: $x = \frac{9}{4}$

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

3. Final Answer

The solutions are $x=0$ and $x=\frac{9}{4}$.