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Simplifying [8(z + 4) + -19] + -2(z + -3) + 2 = 0 Reorder the terms: [8(4 + z) + -19] + -2(z + -3) + 2 = 0 [(4 * 8 + z * 8) + -19] + -2(z + -3) + 2 = 0 [(32 + 8z) + -19] + -2(z + -3) + 2 = 0 Reorder the terms: [32 + -19 + 8z] + -2(z + -3) + 2 = 0 Combine like terms: 32 + -19 = 13 [13 + 8z] + -2(z + -3) + 2 = 0 Remove brackets around [13 + 8z] 13 + 8z + -2(z + -3) + 2 = 0 Reorder the terms: 13 + 8z + -2(-3 + z) + 2 = 0 13 + 8z + (-3 * -2 + z * -2) + 2 = 0 13 + 8z + (6 + -2z) + 2 = 0 Reorder the terms: 13 + 6 + 2 + 8z + -2z = 0 Combine like terms: 13 + 6 = 19 19 + 2 + 8z + -2z = 0 Combine like terms: 19 + 2 = 21 21 + 8z + -2z = 0 Combine like terms: 8z + -2z = 6z 21 + 6z = 0 Solving 21 + 6z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 6z = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 6z = 0 + -21 6z = 0 + -21 Combine like terms: 0 + -21 = -21 6z = -21 Divide each side by '6'. z = -3.5 Simplifying z = -3.5
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