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

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 $\boxed{{\displaystyle 15x^2-43x+30}}$.