<s>[INST] Solve for $x$ in $3\cdot 5^{x^2}+3^{x^2+1}-8\cdot 3^{x^2}=0$ $3\cdot 5^{x^2}+3^{x^2+1}-8\cdot 3^{x^2}=0$
Note that I didn't forget any parenthesis. I copied it as it is in my book.
I tried:
$$3\cdot 5^{x^2}+3^{x^2+1}-8\cdot 3^{x^2}=0 \Leftrightarrow 3\cdot 5^{x^2} - 5 \cdot 3^{2x} = 0 \Leftrightarrow 5 \cdot 3^{x^2} = 3 \cdot 5^{x^2} \Leftrightarrow ???$$
What do I do next?
Also, this $3^{x^2+1}$ confuses me. Does it expand to $3^{x^2}\cdot 3$ or $3^{x^2}\cdot 3^x$?
 [/INST] $$3\cdot 5^{ x^{ 2 } }+3^{ x^{ 2 }+1 }-8\cdot 3^{ x^{ 2 } }=0\\ 3\cdot { \left( \frac { 5 }{ 3 }  \right)  }^{ { x }^{ 2 } }=5\\ { \left( \frac { 5 }{ 3 }  \right)  }^{ { x }^{ 2 } }=\frac { 5 }{ 3 } \quad \Rightarrow { x }^{ 2 }=1\quad \Rightarrow \quad x=\pm 1$$
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