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Simplifying [7(z + 5) + -19] + [3(z + 2) + 4] = 0 Reorder the terms: [7(5 + z) + -19] + [3(z + 2) + 4] = 0 [(5 * 7 + z * 7) + -19] + [3(z + 2) + 4] = 0 [(35 + 7z) + -19] + [3(z + 2) + 4] = 0 Reorder the terms: [35 + -19 + 7z] + [3(z + 2) + 4] = 0 Combine like terms: 35 + -19 = 16 [16 + 7z] + [3(z + 2) + 4] = 0 Remove brackets around [16 + 7z] 16 + 7z + [3(z + 2) + 4] = 0 Reorder the terms: 16 + 7z + [3(2 + z) + 4] = 0 16 + 7z + [(2 * 3 + z * 3) + 4] = 0 16 + 7z + [(6 + 3z) + 4] = 0 Reorder the terms: 16 + 7z + [6 + 4 + 3z] = 0 Combine like terms: 6 + 4 = 10 16 + 7z + [10 + 3z] = 0 Remove brackets around [10 + 3z] 16 + 7z + 10 + 3z = 0 Reorder the terms: 16 + 10 + 7z + 3z = 0 Combine like terms: 16 + 10 = 26 26 + 7z + 3z = 0 Combine like terms: 7z + 3z = 10z 26 + 10z = 0 Solving 26 + 10z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + 10z = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 10z = 0 + -26 10z = 0 + -26 Combine like terms: 0 + -26 = -26 10z = -26 Divide each side by '10'. z = -2.6 Simplifying z = -2.6
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