Tìm x biết (4x – 3)² – 3x(3 – 4x) = 0.

(4x – 3)² – 3x(3 – 4x) = 0

⇔ (3 – 4x)² – 3x(3 – 4x) = 0

⇔ (3 – 4x)(3 – 4x – 3x) = 0

⇔ (3 – 4x)(3 – 7x) = 0

⇔ $\left[ \begin{array}{l}3 - 4x = 0\\3 - 7x = 0\end{array} \right.$

⇔ $\left[ \begin{array}{l}x = \frac{3}{4}\\x = \frac{3}{7}\end{array} \right.$

Vậy S = $\left\{ {\frac{3}{4};\frac{3}{7}} \right\}.$