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Simplifying 2(z + 3) + 3(5 + -3z) = 0 Reorder the terms: 2(3 + z) + 3(5 + -3z) = 0 (3 * 2 + z * 2) + 3(5 + -3z) = 0 (6 + 2z) + 3(5 + -3z) = 0 6 + 2z + (5 * 3 + -3z * 3) = 0 6 + 2z + (15 + -9z) = 0 Reorder the terms: 6 + 15 + 2z + -9z = 0 Combine like terms: 6 + 15 = 21 21 + 2z + -9z = 0 Combine like terms: 2z + -9z = -7z 21 + -7z = 0 Solving 21 + -7z = 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 + -7z = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -7z = 0 + -21 -7z = 0 + -21 Combine like terms: 0 + -21 = -21 -7z = -21 Divide each side by '-7'. z = 3 Simplifying z = 3
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