Question

$$\frac{x^{2}+7x10}{3t+6}=\frac{6x-6}{x^{2}+2x-15}$$

Solve for t

$\left\{\begin{matrix}t=-\frac{x^{4}+2x^{3}-15x^{2}+14xx_{10}-36x+7x_{10}x^{2}-105x_{10}+36}{18\left(1-x\right)}\text{, }&x\neq 3\text{ and }x\neq -5\text{ and }x\neq 1\text{ and }x_{10}\neq -\frac{x^{2}}{7}\text{ and }\left(x_{10}>0\text{ or }|x|\neq \sqrt{-7x_{10}}\right)\\t\neq -2\text{, }&x_{10}=-\frac{1}{7}\text{ and }x=1\end{matrix}\right.$

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