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Simplifying 5(6a + 5b) + 7(3a + 2b) = 0 (6a * 5 + 5b * 5) + 7(3a + 2b) = 0 (30a + 25b) + 7(3a + 2b) = 0 30a + 25b + (3a * 7 + 2b * 7) = 0 30a + 25b + (21a + 14b) = 0 Reorder the terms: 30a + 21a + 25b + 14b = 0 Combine like terms: 30a + 21a = 51a 51a + 25b + 14b = 0 Combine like terms: 25b + 14b = 39b 51a + 39b = 0 Solving 51a + 39b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-39b' to each side of the equation. 51a + 39b + -39b = 0 + -39b Combine like terms: 39b + -39b = 0 51a + 0 = 0 + -39b 51a = 0 + -39b Remove the zero: 51a = -39b Divide each side by '51'. a = -0.7647058824b Simplifying a = -0.7647058824b
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