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Simplifying (2a + 3b)(5c + -1d) = 0 Multiply (2a + 3b) * (5c + -1d) (2a * (5c + -1d) + 3b * (5c + -1d)) = 0 ((5c * 2a + -1d * 2a) + 3b * (5c + -1d)) = 0 ((10ac + -2ad) + 3b * (5c + -1d)) = 0 (10ac + -2ad + (5c * 3b + -1d * 3b)) = 0 (10ac + -2ad + (15bc + -3bd)) = 0 (10ac + -2ad + 15bc + -3bd) = 0 Solving 10ac + -2ad + 15bc + -3bd = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-15bc' to each side of the equation. 10ac + -2ad + 15bc + -15bc + -3bd = 0 + -15bc Combine like terms: 15bc + -15bc = 0 10ac + -2ad + 0 + -3bd = 0 + -15bc 10ac + -2ad + -3bd = 0 + -15bc Remove the zero: 10ac + -2ad + -3bd = -15bc Add '3bd' to each side of the equation. 10ac + -2ad + -3bd + 3bd = -15bc + 3bd Combine like terms: -3bd + 3bd = 0 10ac + -2ad + 0 = -15bc + 3bd 10ac + -2ad = -15bc + 3bd Reorder the terms: 10ac + -2ad + 15bc + -3bd = -15bc + 15bc + 3bd + -3bd Combine like terms: -15bc + 15bc = 0 10ac + -2ad + 15bc + -3bd = 0 + 3bd + -3bd 10ac + -2ad + 15bc + -3bd = 3bd + -3bd Combine like terms: 3bd + -3bd = 0 10ac + -2ad + 15bc + -3bd = 0 The solution to this equation could not be determined.
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