Determine the expanded form of the equation:
$(5 x-6)(3 x-5)$

Step 1 ：Given the equation \((5x - 6)(3x - 5)\).

Step 2 ：We need to expand this equation by applying the distributive property of multiplication over addition.

Step 3 ：First, distribute the first term of the first binomial \(5x\) to the terms in the second binomial \(3x - 5\). This gives us \(15x^2 - 25x\).

Step 4 ：Next, distribute the second term of the first binomial \(-6\) to the terms in the second binomial \(3x - 5\). This gives us \(-18x + 30\).

Step 5 ：Combine the results of the distributions to get the expanded form of the equation: \(15x^2 - 25x - 18x + 30\).

Step 6 ：Simplify the equation by combining like terms to get \(15x^2 - 43x + 30\).

Step 7 ：Final Answer: The expanded form of the equation \((5x - 6)(3x - 5)\) is \(\boxed{15x^2 - 43x + 30}\).