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Simplifying 5(3a + 5b) + 4(2a + -3b) = 0 (3a * 5 + 5b * 5) + 4(2a + -3b) = 0 (15a + 25b) + 4(2a + -3b) = 0 15a + 25b + (2a * 4 + -3b * 4) = 0 15a + 25b + (8a + -12b) = 0 Reorder the terms: 15a + 8a + 25b + -12b = 0 Combine like terms: 15a + 8a = 23a 23a + 25b + -12b = 0 Combine like terms: 25b + -12b = 13b 23a + 13b = 0 Solving 23a + 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. 23a + 13b + -13b = 0 + -13b Combine like terms: 13b + -13b = 0 23a + 0 = 0 + -13b 23a = 0 + -13b Remove the zero: 23a = -13b Divide each side by '23'. a = -0.5652173913b Simplifying a = -0.5652173913b
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