To multiply the expressions \((6x - 5y)\) and \((-3x + 2y)\), we will use the distributive property (also known as the FOIL method for binomials):
\[ (6x - 5y)(-3x + 2y) \]
We will multiply each term in the first expression by each term in the second expression:
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First terms: \[ 6x \cdot (-3x) = -18x^2 \]
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Outer terms: \[ 6x \cdot 2y = 12xy \]
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Inner terms: \[ -5y \cdot (-3x) = 15xy \]
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Last terms: \[ -5y \cdot 2y = -10y^2 \]
Now, combine all these results together:
\[ -18x^2 + 12xy + 15xy - 10y^2 \]
Next, we can combine the like terms (\(12xy\) and \(15xy\)):
\[ -18x^2 + (12xy + 15xy) - 10y^2 = -18x^2 + 27xy - 10y^2 \]
Thus, the final result is:
\[ \boxed{-18x^2 + 27xy - 10y^2} \]