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Simplifying 7(5a + 2b) + 7(6a + 3b) = 0 (5a * 7 + 2b * 7) + 7(6a + 3b) = 0 (35a + 14b) + 7(6a + 3b) = 0 35a + 14b + (6a * 7 + 3b * 7) = 0 35a + 14b + (42a + 21b) = 0 Reorder the terms: 35a + 42a + 14b + 21b = 0 Combine like terms: 35a + 42a = 77a 77a + 14b + 21b = 0 Combine like terms: 14b + 21b = 35b 77a + 35b = 0 Solving 77a + 35b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-35b' to each side of the equation. 77a + 35b + -35b = 0 + -35b Combine like terms: 35b + -35b = 0 77a + 0 = 0 + -35b 77a = 0 + -35b Remove the zero: 77a = -35b Divide each side by '77'. a = -0.4545454545b Simplifying a = -0.4545454545b
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