**Solving the Equation Step-by-Step**

To solve the given equation, we will follow these steps:

1. Expand and simplify both sides of the equation.
2. Combine like terms on each side of the equation.
3. Isolate the variable term on one side of the equation.
4. Solve for the variable by dividing both sides of the equation by the coefficient of the variable.

Now, let's solve the equation step-by-step:

**1. Expand and simplify both sides of the equation:**

On the left side of the equation:
6(3x) - 5(6x) - 5(-1) = 18x - 30x + 5

On the right side of the equation:
3(x) - 5(7x) - 5(-6) = 3x - 35x + 30

**2. Combine like terms on each side of the equation:**

The left side of the equation becomes:
18x - 30x + 5

The right side of the equation becomes:
3x - 35x + 30

**3. Isolate the variable term on one side of the equation:**

We need to combine the x terms on each side of the equation.

The left side of the equation becomes:
-12x + 5

The right side of the equation becomes:
-32x + 30

**4. Solve for the variable by dividing both sides of the equation by the coefficient of the variable:**

To solve for x, we will isolate the x term by subtracting 5 from both sides of the equation:

-12x + 5 - 5 = -32x + 30 - 5

Simplifying both sides of the equation further:

-12x = -32x + 25

Next, we will isolate the x term by adding 32x to both sides of the equation:

-12x + 32x = -32x + 32x + 25

Simplifying both sides of the equation further:

20x = 25

Finally, we will solve for x by dividing both sides of the equation by 20:

x = 25/20

Simplifying the fraction:

x = 5/4

Therefore, the solution to the equation is x = 5/4 or 1.25.

In summary, after expanding, simplifying, combining like terms, isolating the variable term, and solving for x, we find that the solution to the equation 6(3x^2) - 5(6x-1) = 3(x-8) - 5(7x-6) is x = 5/4 or 1.25.