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Simplifying 4(3a + b) + -3(2a + 5b) = 0 (3a * 4 + b * 4) + -3(2a + 5b) = 0 (12a + 4b) + -3(2a + 5b) = 0 12a + 4b + (2a * -3 + 5b * -3) = 0 12a + 4b + (-6a + -15b) = 0 Reorder the terms: 12a + -6a + 4b + -15b = 0 Combine like terms: 12a + -6a = 6a 6a + 4b + -15b = 0 Combine like terms: 4b + -15b = -11b 6a + -11b = 0 Solving 6a + -11b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11b' to each side of the equation. 6a + -11b + 11b = 0 + 11b Combine like terms: -11b + 11b = 0 6a + 0 = 0 + 11b 6a = 0 + 11b Remove the zero: 6a = 11b Divide each side by '6'. a = 1.833333333b Simplifying a = 1.833333333b
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