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Simplifying [9(a + 5) + -16] + -1[3(a + -4) + 2] = 0 Reorder the terms: [9(5 + a) + -16] + -1[3(a + -4) + 2] = 0 [(5 * 9 + a * 9) + -16] + -1[3(a + -4) + 2] = 0 [(45 + 9a) + -16] + -1[3(a + -4) + 2] = 0 Reorder the terms: [45 + -16 + 9a] + -1[3(a + -4) + 2] = 0 Combine like terms: 45 + -16 = 29 [29 + 9a] + -1[3(a + -4) + 2] = 0 Remove brackets around [29 + 9a] 29 + 9a + -1[3(a + -4) + 2] = 0 Reorder the terms: 29 + 9a + -1[3(-4 + a) + 2] = 0 29 + 9a + -1[(-4 * 3 + a * 3) + 2] = 0 29 + 9a + -1[(-12 + 3a) + 2] = 0 Reorder the terms: 29 + 9a + -1[-12 + 2 + 3a] = 0 Combine like terms: -12 + 2 = -10 29 + 9a + -1[-10 + 3a] = 0 29 + 9a + [-10 * -1 + 3a * -1] = 0 29 + 9a + [10 + -3a] = 0 Reorder the terms: 29 + 10 + 9a + -3a = 0 Combine like terms: 29 + 10 = 39 39 + 9a + -3a = 0 Combine like terms: 9a + -3a = 6a 39 + 6a = 0 Solving 39 + 6a = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + 6a = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 6a = 0 + -39 6a = 0 + -39 Combine like terms: 0 + -39 = -39 6a = -39 Divide each side by '6'. a = -6.5 Simplifying a = -6.5
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