To solve the equation \(-4(5m + 6) = 6m + 3(-10m - 4)\), we will follow these steps:
- Distribute both sides of the equation.
- Combine like terms.
- Solve for \(m\).
Starting with the left side:
\[ -4(5m + 6) = -4 \cdot 5m - 4 \cdot 6 = -20m - 24 \]
Now, let's distribute on the right side:
\[ 3(-10m - 4) = 3 \cdot -10m + 3 \cdot -4 = -30m - 12 \]
Now, our equation looks like this:
\[ -20m - 24 = 6m - 30m - 12 \]
Now combine like terms on the right side:
\[ -20m - 24 = -24m - 12 \]
Next, we will add \(24m\) to both sides:
\[ -20m + 24m - 24 = -12 \] \[ 4m - 24 = -12 \]
Now, add 24 to both sides:
\[ 4m = -12 + 24 \] \[ 4m = 12 \]
Finally, divide by 4 to solve for \(m\):
\[ m = \frac{12}{4} = 3 \]
So, the solution is:
\[ \boxed{3} \]
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