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Math AI
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Please solve the problem.

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The problem is to solve:
3^{2x+1} + 4(3^x) - 15 = 0

Here are the step-by-step solutions:

Rewrite the exponential term

We can rewrite 3^{2x+1} as 3^{2x} \cdot 3^1 = 3 \cdot (3^x)^2. Then the equation becomes:
3(3^x)^2 + 4(3^x) - 15 = 0

Substitute a variable

Let y = 3^x. The equation becomes:
3y^2 + 4y - 15 = 0