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Simplifying 3(2a + -7b) + 5(4b + -3a) = 0 (2a * 3 + -7b * 3) + 5(4b + -3a) = 0 (6a + -21b) + 5(4b + -3a) = 0 Reorder the terms: 6a + -21b + 5(-3a + 4b) = 0 6a + -21b + (-3a * 5 + 4b * 5) = 0 6a + -21b + (-15a + 20b) = 0 Reorder the terms: 6a + -15a + -21b + 20b = 0 Combine like terms: 6a + -15a = -9a -9a + -21b + 20b = 0 Combine like terms: -21b + 20b = -1b -9a + -1b = 0 Solving -9a + -1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. -9a + -1b + b = 0 + b Combine like terms: -1b + b = 0 -9a + 0 = 0 + b -9a = 0 + b Remove the zero: -9a = b Divide each side by '-9'. a = -0.1111111111b Simplifying a = -0.1111111111b
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