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Simplifying 4(2a + 3b) + 2(2a + -5b) = 0 (2a * 4 + 3b * 4) + 2(2a + -5b) = 0 (8a + 12b) + 2(2a + -5b) = 0 8a + 12b + (2a * 2 + -5b * 2) = 0 8a + 12b + (4a + -10b) = 0 Reorder the terms: 8a + 4a + 12b + -10b = 0 Combine like terms: 8a + 4a = 12a 12a + 12b + -10b = 0 Combine like terms: 12b + -10b = 2b 12a + 2b = 0 Solving 12a + 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. 12a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 12a + 0 = 0 + -2b 12a = 0 + -2b Remove the zero: 12a = -2b Divide each side by '12'. a = -0.1666666667b Simplifying a = -0.1666666667b
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