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Simplifying 2(a + -2b) + 3(2a + -3b) = 0 (a * 2 + -2b * 2) + 3(2a + -3b) = 0 (2a + -4b) + 3(2a + -3b) = 0 2a + -4b + (2a * 3 + -3b * 3) = 0 2a + -4b + (6a + -9b) = 0 Reorder the terms: 2a + 6a + -4b + -9b = 0 Combine like terms: 2a + 6a = 8a 8a + -4b + -9b = 0 Combine like terms: -4b + -9b = -13b 8a + -13b = 0 Solving 8a + -13b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '13b' to each side of the equation. 8a + -13b + 13b = 0 + 13b Combine like terms: -13b + 13b = 0 8a + 0 = 0 + 13b 8a = 0 + 13b Remove the zero: 8a = 13b Divide each side by '8'. a = 1.625b Simplifying a = 1.625b
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