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Simplifying [7(z + 4) + -19] + -1[3(z + -3) + 2] = 0 Reorder the terms: [7(4 + z) + -19] + -1[3(z + -3) + 2] = 0 [(4 * 7 + z * 7) + -19] + -1[3(z + -3) + 2] = 0 [(28 + 7z) + -19] + -1[3(z + -3) + 2] = 0 Reorder the terms: [28 + -19 + 7z] + -1[3(z + -3) + 2] = 0 Combine like terms: 28 + -19 = 9 [9 + 7z] + -1[3(z + -3) + 2] = 0 Remove brackets around [9 + 7z] 9 + 7z + -1[3(z + -3) + 2] = 0 Reorder the terms: 9 + 7z + -1[3(-3 + z) + 2] = 0 9 + 7z + -1[(-3 * 3 + z * 3) + 2] = 0 9 + 7z + -1[(-9 + 3z) + 2] = 0 Reorder the terms: 9 + 7z + -1[-9 + 2 + 3z] = 0 Combine like terms: -9 + 2 = -7 9 + 7z + -1[-7 + 3z] = 0 9 + 7z + [-7 * -1 + 3z * -1] = 0 9 + 7z + [7 + -3z] = 0 Reorder the terms: 9 + 7 + 7z + -3z = 0 Combine like terms: 9 + 7 = 16 16 + 7z + -3z = 0 Combine like terms: 7z + -3z = 4z 16 + 4z = 0 Solving 16 + 4z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + 4z = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 4z = 0 + -16 4z = 0 + -16 Combine like terms: 0 + -16 = -16 4z = -16 Divide each side by '4'. z = -4 Simplifying z = -4
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