\(3\left(t+2\right)^2+\left(2t-1\right)^2-7\left(t+3\right)\left(t-3\right)=36\\ \Rightarrow3\left(t^2+4t+4\right)+\left(4t^2-4t+1\right)-7\left(t^2-9\right)=36\\ \Rightarrow3t^2+12t+12+4t^2-4t+1-7t^2+63=36\\ \Rightarrow8t+76=36\\ \Rightarrow8t=36-76\\ \Rightarrow8t=-40\\ \Rightarrow t=-5\)
\(3\left(t+2\right)^2+\left(2t-1\right)^2-7\left(t+3\right)\left(t-3\right)=36\)
\(\Rightarrow3\left(t^2+4t+4\right)+\left(4t^2-4t+1\right)-\left(7t+21\right)\left(t-3\right)=36\)
\(\Rightarrow3\left(t^2+4t+4\right)+\left(4t^2-4t+1\right)-7t\left(t-3\right)+21\left(t-3\right)=36\)
\(\Rightarrow3\left(t^2+4t+4\right)+\left(4t^2-4t+1\right)-7t^2+21t+21t-63=36\)
\(\Rightarrow3t^2+12t+12+4t^2-4t+1-7t^2+21t+21t-63=36\)
\(\Rightarrow\left(3t^2+4t^2-7t^2\right)+\left(12t-4t+21t+21t\right)+\left(12+1-63\right)=36\)
\(\Rightarrow50t-50=36\)
\(\Rightarrow50t=50+36\Leftrightarrow50t=86\)
\(\Rightarrow t=\dfrac{86}{50}=\dfrac{43}{25}\)
