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Simplifying 2(3z + -5(2z + -3)) = 4z + -6 Reorder the terms: 2(3z + -5(-3 + 2z)) = 4z + -6 2(3z + (-3 * -5 + 2z * -5)) = 4z + -6 2(3z + (15 + -10z)) = 4z + -6 Reorder the terms: 2(15 + 3z + -10z) = 4z + -6 Combine like terms: 3z + -10z = -7z 2(15 + -7z) = 4z + -6 (15 * 2 + -7z * 2) = 4z + -6 (30 + -14z) = 4z + -6 Reorder the terms: 30 + -14z = -6 + 4z Solving 30 + -14z = -6 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. 30 + -14z + -4z = -6 + 4z + -4z Combine like terms: -14z + -4z = -18z 30 + -18z = -6 + 4z + -4z Combine like terms: 4z + -4z = 0 30 + -18z = -6 + 0 30 + -18z = -6 Add '-30' to each side of the equation. 30 + -30 + -18z = -6 + -30 Combine like terms: 30 + -30 = 0 0 + -18z = -6 + -30 -18z = -6 + -30 Combine like terms: -6 + -30 = -36 -18z = -36 Divide each side by '-18'. z = 2 Simplifying z = 2
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