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Simplifying 6(5a + -1b) + -3(4b + -7a) = 0 (5a * 6 + -1b * 6) + -3(4b + -7a) = 0 (30a + -6b) + -3(4b + -7a) = 0 Reorder the terms: 30a + -6b + -3(-7a + 4b) = 0 30a + -6b + (-7a * -3 + 4b * -3) = 0 30a + -6b + (21a + -12b) = 0 Reorder the terms: 30a + 21a + -6b + -12b = 0 Combine like terms: 30a + 21a = 51a 51a + -6b + -12b = 0 Combine like terms: -6b + -12b = -18b 51a + -18b = 0 Solving 51a + -18b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '18b' to each side of the equation. 51a + -18b + 18b = 0 + 18b Combine like terms: -18b + 18b = 0 51a + 0 = 0 + 18b 51a = 0 + 18b Remove the zero: 51a = 18b Divide each side by '51'. a = 0.3529411765b Simplifying a = 0.3529411765b
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