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Simplifying 5b(7a + -3c) + -1d(7a + -3c) = 0 (7a * 5b + -3c * 5b) + -1d(7a + -3c) = 0 (35ab + -15bc) + -1d(7a + -3c) = 0 35ab + -15bc + (7a * -1d + -3c * -1d) = 0 35ab + -15bc + (-7ad + 3cd) = 0 Reorder the terms: 35ab + -7ad + -15bc + 3cd = 0 Solving 35ab + -7ad + -15bc + 3cd = 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. 35ab + -7ad + -15bc + 15bc + 3cd = 0 + 15bc Combine like terms: -15bc + 15bc = 0 35ab + -7ad + 0 + 3cd = 0 + 15bc 35ab + -7ad + 3cd = 0 + 15bc Remove the zero: 35ab + -7ad + 3cd = 15bc Add '-3cd' to each side of the equation. 35ab + -7ad + 3cd + -3cd = 15bc + -3cd Combine like terms: 3cd + -3cd = 0 35ab + -7ad + 0 = 15bc + -3cd 35ab + -7ad = 15bc + -3cd Reorder the terms: 35ab + -7ad + -15bc + 3cd = 15bc + -15bc + -3cd + 3cd Combine like terms: 15bc + -15bc = 0 35ab + -7ad + -15bc + 3cd = 0 + -3cd + 3cd 35ab + -7ad + -15bc + 3cd = -3cd + 3cd Combine like terms: -3cd + 3cd = 0 35ab + -7ad + -15bc + 3cd = 0 The solution to this equation could not be determined.
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