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Simplifying 7(6a + -1b) + -6(3b + -2a) = 0 (6a * 7 + -1b * 7) + -6(3b + -2a) = 0 (42a + -7b) + -6(3b + -2a) = 0 Reorder the terms: 42a + -7b + -6(-2a + 3b) = 0 42a + -7b + (-2a * -6 + 3b * -6) = 0 42a + -7b + (12a + -18b) = 0 Reorder the terms: 42a + 12a + -7b + -18b = 0 Combine like terms: 42a + 12a = 54a 54a + -7b + -18b = 0 Combine like terms: -7b + -18b = -25b 54a + -25b = 0 Solving 54a + -25b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '25b' to each side of the equation. 54a + -25b + 25b = 0 + 25b Combine like terms: -25b + 25b = 0 54a + 0 = 0 + 25b 54a = 0 + 25b Remove the zero: 54a = 25b Divide each side by '54'. a = 0.462962963b Simplifying a = 0.462962963b
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