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Simplifying 5(2a + 3b) + -3(a + 2b) = 0 (2a * 5 + 3b * 5) + -3(a + 2b) = 0 (10a + 15b) + -3(a + 2b) = 0 10a + 15b + (a * -3 + 2b * -3) = 0 10a + 15b + (-3a + -6b) = 0 Reorder the terms: 10a + -3a + 15b + -6b = 0 Combine like terms: 10a + -3a = 7a 7a + 15b + -6b = 0 Combine like terms: 15b + -6b = 9b 7a + 9b = 0 Solving 7a + 9b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9b' to each side of the equation. 7a + 9b + -9b = 0 + -9b Combine like terms: 9b + -9b = 0 7a + 0 = 0 + -9b 7a = 0 + -9b Remove the zero: 7a = -9b Divide each side by '7'. a = -1.285714286b Simplifying a = -1.285714286b
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