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Simplifying [9(z + 4) + -17] + -1[3(z + -3) + 3] = 0 Reorder the terms: [9(4 + z) + -17] + -1[3(z + -3) + 3] = 0 [(4 * 9 + z * 9) + -17] + -1[3(z + -3) + 3] = 0 [(36 + 9z) + -17] + -1[3(z + -3) + 3] = 0 Reorder the terms: [36 + -17 + 9z] + -1[3(z + -3) + 3] = 0 Combine like terms: 36 + -17 = 19 [19 + 9z] + -1[3(z + -3) + 3] = 0 Remove brackets around [19 + 9z] 19 + 9z + -1[3(z + -3) + 3] = 0 Reorder the terms: 19 + 9z + -1[3(-3 + z) + 3] = 0 19 + 9z + -1[(-3 * 3 + z * 3) + 3] = 0 19 + 9z + -1[(-9 + 3z) + 3] = 0 Reorder the terms: 19 + 9z + -1[-9 + 3 + 3z] = 0 Combine like terms: -9 + 3 = -6 19 + 9z + -1[-6 + 3z] = 0 19 + 9z + [-6 * -1 + 3z * -1] = 0 19 + 9z + [6 + -3z] = 0 Reorder the terms: 19 + 6 + 9z + -3z = 0 Combine like terms: 19 + 6 = 25 25 + 9z + -3z = 0 Combine like terms: 9z + -3z = 6z 25 + 6z = 0 Solving 25 + 6z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 6z = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 6z = 0 + -25 6z = 0 + -25 Combine like terms: 0 + -25 = -25 6z = -25 Divide each side by '6'. z = -4.166666667 Simplifying z = -4.166666667
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