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Simplifying 5(6z + -1) + -3(z + 3) = 12(z + 1) Reorder the terms: 5(-1 + 6z) + -3(z + 3) = 12(z + 1) (-1 * 5 + 6z * 5) + -3(z + 3) = 12(z + 1) (-5 + 30z) + -3(z + 3) = 12(z + 1) Reorder the terms: -5 + 30z + -3(3 + z) = 12(z + 1) -5 + 30z + (3 * -3 + z * -3) = 12(z + 1) -5 + 30z + (-9 + -3z) = 12(z + 1) Reorder the terms: -5 + -9 + 30z + -3z = 12(z + 1) Combine like terms: -5 + -9 = -14 -14 + 30z + -3z = 12(z + 1) Combine like terms: 30z + -3z = 27z -14 + 27z = 12(z + 1) Reorder the terms: -14 + 27z = 12(1 + z) -14 + 27z = (1 * 12 + z * 12) -14 + 27z = (12 + 12z) Solving -14 + 27z = 12 + 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. -14 + 27z + -12z = 12 + 12z + -12z Combine like terms: 27z + -12z = 15z -14 + 15z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -14 + 15z = 12 + 0 -14 + 15z = 12 Add '14' to each side of the equation. -14 + 14 + 15z = 12 + 14 Combine like terms: -14 + 14 = 0 0 + 15z = 12 + 14 15z = 12 + 14 Combine like terms: 12 + 14 = 26 15z = 26 Divide each side by '15'. z = 1.733333333 Simplifying z = 1.733333333
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