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Simplifying 9(z + 2) + -2(z + -3) = 3(z + -2) + 3(z + -3) Reorder the terms: 9(2 + z) + -2(z + -3) = 3(z + -2) + 3(z + -3) (2 * 9 + z * 9) + -2(z + -3) = 3(z + -2) + 3(z + -3) (18 + 9z) + -2(z + -3) = 3(z + -2) + 3(z + -3) Reorder the terms: 18 + 9z + -2(-3 + z) = 3(z + -2) + 3(z + -3) 18 + 9z + (-3 * -2 + z * -2) = 3(z + -2) + 3(z + -3) 18 + 9z + (6 + -2z) = 3(z + -2) + 3(z + -3) Reorder the terms: 18 + 6 + 9z + -2z = 3(z + -2) + 3(z + -3) Combine like terms: 18 + 6 = 24 24 + 9z + -2z = 3(z + -2) + 3(z + -3) Combine like terms: 9z + -2z = 7z 24 + 7z = 3(z + -2) + 3(z + -3) Reorder the terms: 24 + 7z = 3(-2 + z) + 3(z + -3) 24 + 7z = (-2 * 3 + z * 3) + 3(z + -3) 24 + 7z = (-6 + 3z) + 3(z + -3) Reorder the terms: 24 + 7z = -6 + 3z + 3(-3 + z) 24 + 7z = -6 + 3z + (-3 * 3 + z * 3) 24 + 7z = -6 + 3z + (-9 + 3z) Reorder the terms: 24 + 7z = -6 + -9 + 3z + 3z Combine like terms: -6 + -9 = -15 24 + 7z = -15 + 3z + 3z Combine like terms: 3z + 3z = 6z 24 + 7z = -15 + 6z Solving 24 + 7z = -15 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. 24 + 7z + -6z = -15 + 6z + -6z Combine like terms: 7z + -6z = 1z 24 + 1z = -15 + 6z + -6z Combine like terms: 6z + -6z = 0 24 + 1z = -15 + 0 24 + 1z = -15 Add '-24' to each side of the equation. 24 + -24 + 1z = -15 + -24 Combine like terms: 24 + -24 = 0 0 + 1z = -15 + -24 1z = -15 + -24 Combine like terms: -15 + -24 = -39 1z = -39 Divide each side by '1'. z = -39 Simplifying z = -39

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