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Answer
The solutions are \( y=0 \) and \( y=13 \).
Solution
Solve the equation \( 9y(y-13)=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(9y\left(y-13\right)=0\)
- step1: Divide the terms:
\(y\left(y-13\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&y-13=0\\&y=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&y=13\\&y=0\end{align}\)
- step4: Rewrite:
\(y_{1}=0,y_{2}=13\)
The solutions to the equation \(9y(y-13)=0\) are \(y=0\) and \(y=13\).
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Simplify this solution Extra Insights
To solve the equation \( 9y(y-13)=0 \), you can set each factor to zero. This gives you two equations: \( y = 0 \) and \( y - 13 = 0 \), which simplifies to \( y = 13 \). So the solutions are \( y = 0 \) and \( y = 13 \). These values are critical points where the original equation holds true! Graphically, if you were to plot this function, it would cross the y-axis at \( y=0 \) and the line \( y=13 \), creating a curve that shows how the expression behaves. This information can help you understand the roots of polynomials better—it's always great practice to visualize solutions!
