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Simplifying 6(2a + -1b) + -5(3b + -6a) = 0 (2a * 6 + -1b * 6) + -5(3b + -6a) = 0 (12a + -6b) + -5(3b + -6a) = 0 Reorder the terms: 12a + -6b + -5(-6a + 3b) = 0 12a + -6b + (-6a * -5 + 3b * -5) = 0 12a + -6b + (30a + -15b) = 0 Reorder the terms: 12a + 30a + -6b + -15b = 0 Combine like terms: 12a + 30a = 42a 42a + -6b + -15b = 0 Combine like terms: -6b + -15b = -21b 42a + -21b = 0 Solving 42a + -21b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '21b' to each side of the equation. 42a + -21b + 21b = 0 + 21b Combine like terms: -21b + 21b = 0 42a + 0 = 0 + 21b 42a = 0 + 21b Remove the zero: 42a = 21b Divide each side by '42'. a = 0.5b Simplifying a = 0.5b
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