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Simplifying 2(3z + -5(2z + -3)) = 2z + -2 Reorder the terms: 2(3z + -5(-3 + 2z)) = 2z + -2 2(3z + (-3 * -5 + 2z * -5)) = 2z + -2 2(3z + (15 + -10z)) = 2z + -2 Reorder the terms: 2(15 + 3z + -10z) = 2z + -2 Combine like terms: 3z + -10z = -7z 2(15 + -7z) = 2z + -2 (15 * 2 + -7z * 2) = 2z + -2 (30 + -14z) = 2z + -2 Reorder the terms: 30 + -14z = -2 + 2z Solving 30 + -14z = -2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. 30 + -14z + -2z = -2 + 2z + -2z Combine like terms: -14z + -2z = -16z 30 + -16z = -2 + 2z + -2z Combine like terms: 2z + -2z = 0 30 + -16z = -2 + 0 30 + -16z = -2 Add '-30' to each side of the equation. 30 + -30 + -16z = -2 + -30 Combine like terms: 30 + -30 = 0 0 + -16z = -2 + -30 -16z = -2 + -30 Combine like terms: -2 + -30 = -32 -16z = -32 Divide each side by '-16'. z = 2 Simplifying z = 2
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