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Simplifying (2a + 7b)(5c + -3d) = 0 Multiply (2a + 7b) * (5c + -3d) (2a * (5c + -3d) + 7b * (5c + -3d)) = 0 ((5c * 2a + -3d * 2a) + 7b * (5c + -3d)) = 0 ((10ac + -6ad) + 7b * (5c + -3d)) = 0 (10ac + -6ad + (5c * 7b + -3d * 7b)) = 0 (10ac + -6ad + (35bc + -21bd)) = 0 (10ac + -6ad + 35bc + -21bd) = 0 Solving 10ac + -6ad + 35bc + -21bd = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-35bc' to each side of the equation. 10ac + -6ad + 35bc + -35bc + -21bd = 0 + -35bc Combine like terms: 35bc + -35bc = 0 10ac + -6ad + 0 + -21bd = 0 + -35bc 10ac + -6ad + -21bd = 0 + -35bc Remove the zero: 10ac + -6ad + -21bd = -35bc Add '21bd' to each side of the equation. 10ac + -6ad + -21bd + 21bd = -35bc + 21bd Combine like terms: -21bd + 21bd = 0 10ac + -6ad + 0 = -35bc + 21bd 10ac + -6ad = -35bc + 21bd Reorder the terms: 10ac + -6ad + 35bc + -21bd = -35bc + 35bc + 21bd + -21bd Combine like terms: -35bc + 35bc = 0 10ac + -6ad + 35bc + -21bd = 0 + 21bd + -21bd 10ac + -6ad + 35bc + -21bd = 21bd + -21bd Combine like terms: 21bd + -21bd = 0 10ac + -6ad + 35bc + -21bd = 0 The solution to this equation could not be determined.
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