We are asked to solve the equation $6(3x-4) - 10(x-3) = 10(2x-3)$ for $x$.

1. Problem Description

We are asked to solve the equation $6(3x-4) - 10(x-3) = 10(2x-3)$ for $x$.

2. Solution Steps

First, we distribute the constants outside the parentheses into the terms inside the parentheses.

$6(3x-4) = 6(3x) - 6(4) = 18x - 24$

$-10(x-3) = -10(x) - 10(-3) = -10x + 30$

$10(2x-3) = 10(2x) - 10(3) = 20x - 30$

Substituting these back into the original equation gives:

$18x - 24 - 10x + 30 = 20x - 30$

Now, we combine like terms on the left side of the equation:

$(18x - 10x) + (-24 + 30) = 20x - 30$

$8x + 6 = 20x - 30$

Next, we want to isolate the $x$ terms. We can subtract $8x$ from both sides of the equation:

$8x + 6 - 8x = 20x - 30 - 8x$

$6 = 12x - 30$

Now, we add $30$ to both sides of the equation:

$6 + 30 = 12x - 30 + 30$

$36 = 12x$

Finally, we divide both sides by $12$ to solve for $x$:

$\frac{36}{12} = \frac{12x}{12}$

$3 = x$

So, $x=3$.

3. Final Answer

$x = 3$