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The given equation is:

\[
5 \cdot 6^x - 3^{x+1} \cdot 2^x = 72
\]

Let's break down the equation and solve for \( x \).

1. \( 5 \cdot 6^x \) remains as it is.
2. Rewrite \( 3^{x+1} \cdot 2^x \): This can be expressed as \( 3 \cdot 3^x \cdot 2^x \).

This gives the updated equation:

\[
5 \cdot 6^x - 3 \cdot 3^x \cdot 2^x = 72
\]

Now, let's try to simplify and solve this. I will perform the calculations step by step.The solution to the equation \( 5 \cdot 6^x - 3^{x+1} \cdot 2^x = 72 \) is \( x = 2 \).

Would you like further details or have any questions about the steps?

Here are 5 related questions for you to explore:
1. How can you verify that \( x = 2 \) satisfies the original equation?
2. What method is typically used to solve exponential equations like this one?
3. How would the solution change if one of the constants in the equation were different?
4. Can this type of equation be solved graphically as well?
5. How do the properties of exponents help simplify expressions like \( 3^{x+1} \cdot 2^x \)?

**Tip:** When solving exponential equations, expressing all terms with the same base or factoring is often a useful strategy to simplify the equation.

Solve the equation: 5 * 6^x - 3^(x+1) * 2^x = 72.

This page explains how to solve the exponential equation 5 * 6^x - 3^(x+1) * 2^x = 72 using the laws of exponents. The solution includes breaking down complex terms and simplifying expressions to find the value of x. Suitable for students in Grades 9-12.

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