Solution
We want to solve
[tex]27x^2=9x\text{ using zero product thorem}[/tex]The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.
For the question,
[tex]\begin{gathered} 27x^2=9x \\ \text{Divide both sides by }9 \\ 3x^2=x \\ \text{Subtract x from both sides} \\ 3x^2-x=0 \\ \text{Factorize} \\ x(3x-1)=0 \\ \text{Applying the zero theroem, we have} \\ x=0\text{ or 3x-1=0} \\ x=0\text{ or 3x = 1} \\ x=0\text{ or x = }\frac{1}{3} \end{gathered}[/tex]The answer is x = 0 and x = 1/3
