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Simplifying 6(5a + -1b) + -5(4b + -7a) = 0 (5a * 6 + -1b * 6) + -5(4b + -7a) = 0 (30a + -6b) + -5(4b + -7a) = 0 Reorder the terms: 30a + -6b + -5(-7a + 4b) = 0 30a + -6b + (-7a * -5 + 4b * -5) = 0 30a + -6b + (35a + -20b) = 0 Reorder the terms: 30a + 35a + -6b + -20b = 0 Combine like terms: 30a + 35a = 65a 65a + -6b + -20b = 0 Combine like terms: -6b + -20b = -26b 65a + -26b = 0 Solving 65a + -26b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '26b' to each side of the equation. 65a + -26b + 26b = 0 + 26b Combine like terms: -26b + 26b = 0 65a + 0 = 0 + 26b 65a = 0 + 26b Remove the zero: 65a = 26b Divide each side by '65'. a = 0.4b Simplifying a = 0.4b
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