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Simplifying 4(2a + 3b) + 5(2a + 4b) = 0 (2a * 4 + 3b * 4) + 5(2a + 4b) = 0 (8a + 12b) + 5(2a + 4b) = 0 8a + 12b + (2a * 5 + 4b * 5) = 0 8a + 12b + (10a + 20b) = 0 Reorder the terms: 8a + 10a + 12b + 20b = 0 Combine like terms: 8a + 10a = 18a 18a + 12b + 20b = 0 Combine like terms: 12b + 20b = 32b 18a + 32b = 0 Solving 18a + 32b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-32b' to each side of the equation. 18a + 32b + -32b = 0 + -32b Combine like terms: 32b + -32b = 0 18a + 0 = 0 + -32b 18a = 0 + -32b Remove the zero: 18a = -32b Divide each side by '18'. a = -1.777777778b Simplifying a = -1.777777778b
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