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 $ax^{2}+bx+c=0$.
$$4k^{2}+6k=0$$
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.
$$k=\frac{-6±\sqrt{6^{2}}}{2\times 4}$$
Take the square root of $6^{2}$.
$$k=\frac{-6±6}{2\times 4}$$
Multiply $2$ times $4$.
$$k=\frac{-6±6}{8}$$
Now solve the equation $k=\frac{-6±6}{8}$ when $±$ is plus. Add $-6$ to $6$.
$$k=\frac{0}{8}$$
Divide $0$ by $8$.
$$k=0$$
Now solve the equation $k=\frac{-6±6}{8}$ when $±$ is minus. Subtract $6$ from $-6$.
$$k=-\frac{12}{8}$$
Reduce the fraction $\frac{-12}{8}$ to lowest terms by extracting and canceling out $4$.
$$k=-\frac{3}{2}$$
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 $-\frac{3}{2}$ for $x_{2}$.
