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Simplifying 12(3a + 5b) + -7(6a + 3b) = 0 (3a * 12 + 5b * 12) + -7(6a + 3b) = 0 (36a + 60b) + -7(6a + 3b) = 0 36a + 60b + (6a * -7 + 3b * -7) = 0 36a + 60b + (-42a + -21b) = 0 Reorder the terms: 36a + -42a + 60b + -21b = 0 Combine like terms: 36a + -42a = -6a -6a + 60b + -21b = 0 Combine like terms: 60b + -21b = 39b -6a + 39b = 0 Solving -6a + 39b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-39b' to each side of the equation. -6a + 39b + -39b = 0 + -39b Combine like terms: 39b + -39b = 0 -6a + 0 = 0 + -39b -6a = 0 + -39b Remove the zero: -6a = -39b Divide each side by '-6'. a = 6.5b Simplifying a = 6.5b
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