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Simplifying (5a + -2b + 3c)(6a + -3b + 2c) = 0 Multiply (5a + -2b + 3c) * (6a + -3b + 2c) (5a * (6a + -3b + 2c) + -2b * (6a + -3b + 2c) + 3c * (6a + -3b + 2c)) = 0 ((6a * 5a + -3b * 5a + 2c * 5a) + -2b * (6a + -3b + 2c) + 3c * (6a + -3b + 2c)) = 0 Reorder the terms: ((-15ab + 10ac + 30a2) + -2b * (6a + -3b + 2c) + 3c * (6a + -3b + 2c)) = 0 ((-15ab + 10ac + 30a2) + -2b * (6a + -3b + 2c) + 3c * (6a + -3b + 2c)) = 0 (-15ab + 10ac + 30a2 + (6a * -2b + -3b * -2b + 2c * -2b) + 3c * (6a + -3b + 2c)) = 0 Reorder the terms: (-15ab + 10ac + 30a2 + (-12ab + -4bc + 6b2) + 3c * (6a + -3b + 2c)) = 0 (-15ab + 10ac + 30a2 + (-12ab + -4bc + 6b2) + 3c * (6a + -3b + 2c)) = 0 (-15ab + 10ac + 30a2 + -12ab + -4bc + 6b2 + (6a * 3c + -3b * 3c + 2c * 3c)) = 0 (-15ab + 10ac + 30a2 + -12ab + -4bc + 6b2 + (18ac + -9bc + 6c2)) = 0 Reorder the terms: (-15ab + -12ab + 10ac + 18ac + 30a2 + -4bc + -9bc + 6b2 + 6c2) = 0 Combine like terms: -15ab + -12ab = -27ab (-27ab + 10ac + 18ac + 30a2 + -4bc + -9bc + 6b2 + 6c2) = 0 Combine like terms: 10ac + 18ac = 28ac (-27ab + 28ac + 30a2 + -4bc + -9bc + 6b2 + 6c2) = 0 Combine like terms: -4bc + -9bc = -13bc (-27ab + 28ac + 30a2 + -13bc + 6b2 + 6c2) = 0 Solving -27ab + 28ac + 30a2 + -13bc + 6b2 + 6c2 = 0 Solving for variable 'a'. The solution to this equation could not be determined.
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