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 $ax^{2}+bx+c=0$.
$$35t^{2}+14t=0$$
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.
$$t=\frac{-14±\sqrt{14^{2}}}{2\times 35}$$
Take the square root of $14^{2}$.
$$t=\frac{-14±14}{2\times 35}$$
Multiply $2$ times $35$.
$$t=\frac{-14±14}{70}$$
Now solve the equation $t=\frac{-14±14}{70}$ when $±$ is plus. Add $-14$ to $14$.
$$t=\frac{0}{70}$$
Divide $0$ by $70$.
$$t=0$$
Now solve the equation $t=\frac{-14±14}{70}$ when $±$ is minus. Subtract $14$ from $-14$.
$$t=-\frac{28}{70}$$
Reduce the fraction $\frac{-28}{70}$ to lowest terms by extracting and canceling out $14$.
$$t=-\frac{2}{5}$$
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 $-\frac{2}{5}$ for $x_{2}$.
