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Simplifying 4(3a + 5b + 7) + -1(8b + 21) = 0 Reorder the terms: 4(7 + 3a + 5b) + -1(8b + 21) = 0 (7 * 4 + 3a * 4 + 5b * 4) + -1(8b + 21) = 0 (28 + 12a + 20b) + -1(8b + 21) = 0 Reorder the terms: 28 + 12a + 20b + -1(21 + 8b) = 0 28 + 12a + 20b + (21 * -1 + 8b * -1) = 0 28 + 12a + 20b + (-21 + -8b) = 0 Reorder the terms: 28 + -21 + 12a + 20b + -8b = 0 Combine like terms: 28 + -21 = 7 7 + 12a + 20b + -8b = 0 Combine like terms: 20b + -8b = 12b 7 + 12a + 12b = 0 Solving 7 + 12a + 12b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + 12a + -7 + 12b = 0 + -7 Reorder the terms: 7 + -7 + 12a + 12b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 12a + 12b = 0 + -7 12a + 12b = 0 + -7 Combine like terms: 0 + -7 = -7 12a + 12b = -7 Add '-12b' to each side of the equation. 12a + 12b + -12b = -7 + -12b Combine like terms: 12b + -12b = 0 12a + 0 = -7 + -12b 12a = -7 + -12b Divide each side by '12'. a = -0.5833333333 + -1b Simplifying a = -0.5833333333 + -1b
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