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Simplifying [7(z + 5) + -17] + [3(z + -2) + 2] = 0 Reorder the terms: [7(5 + z) + -17] + [3(z + -2) + 2] = 0 [(5 * 7 + z * 7) + -17] + [3(z + -2) + 2] = 0 [(35 + 7z) + -17] + [3(z + -2) + 2] = 0 Reorder the terms: [35 + -17 + 7z] + [3(z + -2) + 2] = 0 Combine like terms: 35 + -17 = 18 [18 + 7z] + [3(z + -2) + 2] = 0 Remove brackets around [18 + 7z] 18 + 7z + [3(z + -2) + 2] = 0 Reorder the terms: 18 + 7z + [3(-2 + z) + 2] = 0 18 + 7z + [(-2 * 3 + z * 3) + 2] = 0 18 + 7z + [(-6 + 3z) + 2] = 0 Reorder the terms: 18 + 7z + [-6 + 2 + 3z] = 0 Combine like terms: -6 + 2 = -4 18 + 7z + [-4 + 3z] = 0 Remove brackets around [-4 + 3z] 18 + 7z + -4 + 3z = 0 Reorder the terms: 18 + -4 + 7z + 3z = 0 Combine like terms: 18 + -4 = 14 14 + 7z + 3z = 0 Combine like terms: 7z + 3z = 10z 14 + 10z = 0 Solving 14 + 10z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 10z = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 10z = 0 + -14 10z = 0 + -14 Combine like terms: 0 + -14 = -14 10z = -14 Divide each side by '10'. z = -1.4 Simplifying z = -1.4
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