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Simplifying 4(2a + -3b) + -5(a + -2b) = 0 (2a * 4 + -3b * 4) + -5(a + -2b) = 0 (8a + -12b) + -5(a + -2b) = 0 8a + -12b + (a * -5 + -2b * -5) = 0 8a + -12b + (-5a + 10b) = 0 Reorder the terms: 8a + -5a + -12b + 10b = 0 Combine like terms: 8a + -5a = 3a 3a + -12b + 10b = 0 Combine like terms: -12b + 10b = -2b 3a + -2b = 0 Solving 3a + -2b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 3a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 3a + 0 = 0 + 2b 3a = 0 + 2b Remove the zero: 3a = 2b Divide each side by '3'. a = 0.6666666667b Simplifying a = 0.6666666667b
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