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Simplifying 7(5a + 3b) + 7(2a + 4b) = 0 (5a * 7 + 3b * 7) + 7(2a + 4b) = 0 (35a + 21b) + 7(2a + 4b) = 0 35a + 21b + (2a * 7 + 4b * 7) = 0 35a + 21b + (14a + 28b) = 0 Reorder the terms: 35a + 14a + 21b + 28b = 0 Combine like terms: 35a + 14a = 49a 49a + 21b + 28b = 0 Combine like terms: 21b + 28b = 49b 49a + 49b = 0 Solving 49a + 49b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-49b' to each side of the equation. 49a + 49b + -49b = 0 + -49b Combine like terms: 49b + -49b = 0 49a + 0 = 0 + -49b 49a = 0 + -49b Remove the zero: 49a = -49b Divide each side by '49'. a = -1b Simplifying a = -1b
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