Calculate $1250$ to the power of $3$ and get $1953125000$.
$$factor(27-1953125000-135a+225a^{2})$$
Subtract $1953125000$ from $27$ to get $-1953124973$.
$$factor(-1953124973-135a+225a^{2})$$
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 $ax^{2}+bx+c=0$.
$$225a^{2}-135a-1953124973=0$$
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.
Now solve the equation $a=\frac{135±15\sqrt{7812499973}}{450}$ when $±$ is plus. Add $135$ to $15\sqrt{7812499973}$.
$$a=\frac{15\sqrt{7812499973}+135}{450}$$
Divide $135+15\sqrt{7812499973}$ by $450$.
$$a=\frac{\sqrt{7812499973}}{30}+\frac{3}{10}$$
Now solve the equation $a=\frac{135±15\sqrt{7812499973}}{450}$ when $±$ is minus. Subtract $15\sqrt{7812499973}$ from $135$.
$$a=\frac{135-15\sqrt{7812499973}}{450}$$
Divide $135-15\sqrt{7812499973}$ by $450$.
$$a=-\frac{\sqrt{7812499973}}{30}+\frac{3}{10}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{3}{10}+\frac{\sqrt{7812499973}}{30}$ for $x_{1}$ and $\frac{3}{10}-\frac{\sqrt{7812499973}}{30}$ for $x_{2}$.
