Solve the Following Quadratic Equation by Factorization

Question:

\[ abx^2+(b^2-ac)x-bc=0 \]

Solution

Given,

\[ abx^2+(b^2-ac)x-bc=0 \]

Split the middle term:

\[ abx^2+b^2x-acx-bc=0 \]

Taking common factors:

\[ bx(ax+b)-c(ax+b)=0 \] \[ (ax+b)(bx-c)=0 \]

Therefore,

\[ ax+b=0 \] or \[ bx-c=0 \] \[ x=-\frac{b}{a} \] or \[ x=\frac{c}{b} \]

Final Answer

\[ \boxed{x=-\frac{b}{a} \quad \text{or} \quad x=\frac{c}{b}} \]