To solve the equation \( 7(5x + 2) = -4(6 - 5x) \), we will first distribute both sides.
Starting with the left side:
\[ 7(5x + 2) = 7 \cdot 5x + 7 \cdot 2 = 35x + 14 \]
Now for the right side:
\[ -4(6 - 5x) = -4 \cdot 6 + -4 \cdot (-5x) = -24 + 20x \]
Now we can set the left side equal to the right side:
\[ 35x + 14 = -24 + 20x \]
Next, we'll isolate the variable \( x \) by getting all \( x \) terms on one side and constant terms on the other side. First, we'll subtract \( 20x \) from both sides:
\[ 35x - 20x + 14 = -24 \] \[ 15x + 14 = -24 \]
Next, we subtract 14 from both sides:
\[ 15x = -24 - 14 \] \[ 15x = -38 \]
Now we divide both sides by 15 to solve for \( x \):
\[ x = \frac{-38}{15} \]
Thus, the solution is:
\[ \boxed{\frac{-38}{15}} \]
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