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Simplifying 4(2a + 3b) + 2(3a + -3b) = 0 (2a * 4 + 3b * 4) + 2(3a + -3b) = 0 (8a + 12b) + 2(3a + -3b) = 0 8a + 12b + (3a * 2 + -3b * 2) = 0 8a + 12b + (6a + -6b) = 0 Reorder the terms: 8a + 6a + 12b + -6b = 0 Combine like terms: 8a + 6a = 14a 14a + 12b + -6b = 0 Combine like terms: 12b + -6b = 6b 14a + 6b = 0 Solving 14a + 6b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. 14a + 6b + -6b = 0 + -6b Combine like terms: 6b + -6b = 0 14a + 0 = 0 + -6b 14a = 0 + -6b Remove the zero: 14a = -6b Divide each side by '14'. a = -0.4285714286b Simplifying a = -0.4285714286b
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