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Simplifying [7(z + 5) + -19] + [3(z + -3) + 2] = 0 Reorder the terms: [7(5 + z) + -19] + [3(z + -3) + 2] = 0 [(5 * 7 + z * 7) + -19] + [3(z + -3) + 2] = 0 [(35 + 7z) + -19] + [3(z + -3) + 2] = 0 Reorder the terms: [35 + -19 + 7z] + [3(z + -3) + 2] = 0 Combine like terms: 35 + -19 = 16 [16 + 7z] + [3(z + -3) + 2] = 0 Remove brackets around [16 + 7z] 16 + 7z + [3(z + -3) + 2] = 0 Reorder the terms: 16 + 7z + [3(-3 + z) + 2] = 0 16 + 7z + [(-3 * 3 + z * 3) + 2] = 0 16 + 7z + [(-9 + 3z) + 2] = 0 Reorder the terms: 16 + 7z + [-9 + 2 + 3z] = 0 Combine like terms: -9 + 2 = -7 16 + 7z + [-7 + 3z] = 0 Remove brackets around [-7 + 3z] 16 + 7z + -7 + 3z = 0 Reorder the terms: 16 + -7 + 7z + 3z = 0 Combine like terms: 16 + -7 = 9 9 + 7z + 3z = 0 Combine like terms: 7z + 3z = 10z 9 + 10z = 0 Solving 9 + 10z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 10z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 10z = 0 + -9 10z = 0 + -9 Combine like terms: 0 + -9 = -9 10z = -9 Divide each side by '10'. z = -0.9 Simplifying z = -0.9
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