To solve the equation
\[ -6(-8x + 7) = 7(5x + 6), \]
let's start by simplifying both sides.
Step 1: Distribute on the left side.
\[ -6(-8x) + (-6)(7) = 48x - 42 \]
So, the left side becomes:
\[ 48x - 42. \]
Step 2: Distribute on the right side.
\[ 7(5x) + 7(6) = 35x + 42. \]
So, the right side becomes:
\[ 35x + 42. \]
Step 3: Rewrite the equation with the simplified expressions.
We now have:
\[ 48x - 42 = 35x + 42. \]
Step 4: Move all terms involving \(x\) to one side and constant terms to the other side.
Subtract \(35x\) from both sides:
\[ 48x - 35x - 42 = 42. \]
This simplifies to:
\[ 13x - 42 = 42. \]
Next, add \(42\) to both sides:
\[ 13x = 42 + 42. \]
This simplifies to:
\[ 13x = 84. \]
Step 5: Solve for \(x\).
Divide both sides by \(13\):
\[ x = \frac{84}{13}. \]
Thus, the solution in its simplest form is:
\[ \boxed{\frac{84}{13}}. \]
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