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Simplifying 3(4a + -2b) + -5(3a + b) = 0 (4a * 3 + -2b * 3) + -5(3a + b) = 0 (12a + -6b) + -5(3a + b) = 0 12a + -6b + (3a * -5 + b * -5) = 0 12a + -6b + (-15a + -5b) = 0 Reorder the terms: 12a + -15a + -6b + -5b = 0 Combine like terms: 12a + -15a = -3a -3a + -6b + -5b = 0 Combine like terms: -6b + -5b = -11b -3a + -11b = 0 Solving -3a + -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. -3a + -11b + 11b = 0 + 11b Combine like terms: -11b + 11b = 0 -3a + 0 = 0 + 11b -3a = 0 + 11b Remove the zero: -3a = 11b Divide each side by '-3'. a = -3.666666667b Simplifying a = -3.666666667b
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