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Simplifying [7(z + 4) + -16] + -1[2(z + -3) + 1] = 0 Reorder the terms: [7(4 + z) + -16] + -1[2(z + -3) + 1] = 0 [(4 * 7 + z * 7) + -16] + -1[2(z + -3) + 1] = 0 [(28 + 7z) + -16] + -1[2(z + -3) + 1] = 0 Reorder the terms: [28 + -16 + 7z] + -1[2(z + -3) + 1] = 0 Combine like terms: 28 + -16 = 12 [12 + 7z] + -1[2(z + -3) + 1] = 0 Remove brackets around [12 + 7z] 12 + 7z + -1[2(z + -3) + 1] = 0 Reorder the terms: 12 + 7z + -1[2(-3 + z) + 1] = 0 12 + 7z + -1[(-3 * 2 + z * 2) + 1] = 0 12 + 7z + -1[(-6 + 2z) + 1] = 0 Reorder the terms: 12 + 7z + -1[-6 + 1 + 2z] = 0 Combine like terms: -6 + 1 = -5 12 + 7z + -1[-5 + 2z] = 0 12 + 7z + [-5 * -1 + 2z * -1] = 0 12 + 7z + [5 + -2z] = 0 Reorder the terms: 12 + 5 + 7z + -2z = 0 Combine like terms: 12 + 5 = 17 17 + 7z + -2z = 0 Combine like terms: 7z + -2z = 5z 17 + 5z = 0 Solving 17 + 5z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 5z = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 5z = 0 + -17 5z = 0 + -17 Combine like terms: 0 + -17 = -17 5z = -17 Divide each side by '5'. z = -3.4 Simplifying z = -3.4
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