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Simplifying 6(3a + -1b) + -6(5b + -7a) = 0 (3a * 6 + -1b * 6) + -6(5b + -7a) = 0 (18a + -6b) + -6(5b + -7a) = 0 Reorder the terms: 18a + -6b + -6(-7a + 5b) = 0 18a + -6b + (-7a * -6 + 5b * -6) = 0 18a + -6b + (42a + -30b) = 0 Reorder the terms: 18a + 42a + -6b + -30b = 0 Combine like terms: 18a + 42a = 60a 60a + -6b + -30b = 0 Combine like terms: -6b + -30b = -36b 60a + -36b = 0 Solving 60a + -36b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '36b' to each side of the equation. 60a + -36b + 36b = 0 + 36b Combine like terms: -36b + 36b = 0 60a + 0 = 0 + 36b 60a = 0 + 36b Remove the zero: 60a = 36b Divide each side by '60'. a = 0.6b Simplifying a = 0.6b
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