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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 = 19b 6a + 19b = 0 Solving 6a + 19b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-19b' to each side of the equation. 6a + 19b + -19b = 0 + -19b Combine like terms: 19b + -19b = 0 6a + 0 = 0 + -19b 6a = 0 + -19b Remove the zero: 6a = -19b Divide each side by '6'. a = -3.166666667b Simplifying a = -3.166666667b
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