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Simplifying 5(2a + b) + -2(3a + -5b) = 0 (2a * 5 + b * 5) + -2(3a + -5b) = 0 (10a + 5b) + -2(3a + -5b) = 0 10a + 5b + (3a * -2 + -5b * -2) = 0 10a + 5b + (-6a + 10b) = 0 Reorder the terms: 10a + -6a + 5b + 10b = 0 Combine like terms: 10a + -6a = 4a 4a + 5b + 10b = 0 Combine like terms: 5b + 10b = 15b 4a + 15b = 0 Solving 4a + 15b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-15b' to each side of the equation. 4a + 15b + -15b = 0 + -15b Combine like terms: 15b + -15b = 0 4a + 0 = 0 + -15b 4a = 0 + -15b Remove the zero: 4a = -15b Divide each side by '4'. a = -3.75b Simplifying a = -3.75b
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