Solve {l}{P{(x)}*P{(x+7)}=x^2-5x-6}{a=P{(10)}}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { P {(x)} \cdot P {(x + 7)} = x ^ {2} - 5 x - 6 }\\ { a = P {(10)} }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{49a^{4}+4600a^{2}+490000}-7a^{2}-500}{2\left(a^{2}-100\right)}\text{; }x=-\frac{\sqrt{49a^{4}+4600a^{2}+490000}+7a^{2}+500}{2\left(a^{2}-100\right)}\text{, }&a=c\text{ and }P=\frac{c}{10}\text{ and }b=c\text{ and }c\neq 10\text{ and }c\neq -10\\x=-\frac{6}{7P^{2}+5}\text{, }&\left(c=-10\text{ and }b=-10\text{ and }a=-10\text{ and }P=-1\right)\text{ or }\left(c=10\text{ and }b=10\text{ and }a=10\text{ and }P=1\right)\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{49b^{4}+4600b^{2}+490000}-7b^{2}-500}{2\left(b^{2}-100\right)}\text{; }x=-\frac{\sqrt{49b^{4}+4600b^{2}+490000}+7b^{2}+500}{2\left(b^{2}-100\right)}\text{, }&c=b\text{ and }a=b\text{ and }P=\frac{b}{10}\text{ and }|b|\neq 10\\x=-\frac{6}{7P^{2}+5}\text{, }&\left(c=10\text{ and }b=10\text{ and }P=1\text{ and }a=10\right)\text{ or }\left(c=-10\text{ and }b=-10\text{ and }P=-1\text{ and }a=-10\right)\end{matrix}\right.$$