Solve the equation $4x^2 = 9x$.

1. Problem Description

Solve the equation $4x^2 = 9x$.

2. Solution Steps

We want to solve for $x$ in the equation $4x^2 = 9x$. First, we move all terms to one side of the equation to set it equal to zero:

$4x^2 - 9x = 0$

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

$x(4x - 9) = 0$

Now we use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Thus, we have two possible equations:

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

The first equation, $x = 0$, is one solution.

For the second equation, $4x - 9 = 0$, we add 9 to both sides:

$4x = 9$

Then, we divide both sides by 4:

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

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

3. Final Answer

$x = 0, \frac{9}{4}$