Question

find the real solutions by factoring.
$9x^3 = 4x^2$

Explanation:

Step1: Move all terms to left side

$9x^3 - 4x^2 = 0$

Step2: Factor out common term $x^2$

$x^2(9x - 4) = 0$

Step3: Set each factor to 0

$x^2 = 0$ and $9x - 4 = 0$

Step4: Solve for $x$

For $x^2=0$: $x=0$; for $9x-4=0$: $x=\frac{4}{9}$

Answer:

$x=0$ (with multiplicity 2) and $x=\frac{4}{9}$