Quadratic polynomial can be factored using the transformation $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$, where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation $ax^{2}+bx+c=0$.
$$-13y^{2}+24y=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
$$y=\frac{-24±\sqrt{24^{2}}}{2\left(-13\right)}$$
Take the square root of $24^{2}$.
$$y=\frac{-24±24}{2\left(-13\right)}$$
Multiply $2$ times $-13$.
$$y=\frac{-24±24}{-26}$$
Now solve the equation $y=\frac{-24±24}{-26}$ when $±$ is plus. Add $-24$ to $24$.
$$y=\frac{0}{-26}$$
Divide $0$ by $-26$.
$$y=0$$
Now solve the equation $y=\frac{-24±24}{-26}$ when $±$ is minus. Subtract $24$ from $-24$.
$$y=-\frac{48}{-26}$$
Reduce the fraction $\frac{-48}{-26}$ to lowest terms by extracting and canceling out $2$.
$$y=\frac{24}{13}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $0$ for $x_{1}$ and $\frac{24}{13}$ for $x_{2}$.
$$-13y^{2}+24y=-13y\left(y-\frac{24}{13}\right)$$
Subtract $\frac{24}{13}$ from $y$ by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.
$$-13y^{2}+24y=-13y\times \frac{-13y+24}{-13}$$
Cancel out $13$, the greatest common factor in $-13$ and $-13$.
