Question

Solve the following equation by factorisation: $15y^2=41y-14$

Answer 1

Solve by factorisation

$$\begin{gathered} \Rightarrow 15y^2=41y-14 \\ \Rightarrow 15y^2-41y+14=0 \\ \Rightarrow 15y^2-6y-35y+14=0 \\ \Rightarrow 3y(5y-2)-7(5y-2)=0 \\ \Rightarrow (3y-7)(5y-2)=0 \\ \Rightarrow 3y-7=0or5y-2=0 \\ \Rightarrow y=\frac{7}{3}ory=\frac{2}{5} \end{gathered}$$

Thus, the roots of the equation by factorisation are $\frac{\mathbf{7}}{\mathbf{3}}$ and $\frac{\mathbf{2}}{\mathbf{5}}$ .