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Simplifying -8(z + 3) + 5(3z + -3) = 6(z + -3) + 14 Reorder the terms: -8(3 + z) + 5(3z + -3) = 6(z + -3) + 14 (3 * -8 + z * -8) + 5(3z + -3) = 6(z + -3) + 14 (-24 + -8z) + 5(3z + -3) = 6(z + -3) + 14 Reorder the terms: -24 + -8z + 5(-3 + 3z) = 6(z + -3) + 14 -24 + -8z + (-3 * 5 + 3z * 5) = 6(z + -3) + 14 -24 + -8z + (-15 + 15z) = 6(z + -3) + 14 Reorder the terms: -24 + -15 + -8z + 15z = 6(z + -3) + 14 Combine like terms: -24 + -15 = -39 -39 + -8z + 15z = 6(z + -3) + 14 Combine like terms: -8z + 15z = 7z -39 + 7z = 6(z + -3) + 14 Reorder the terms: -39 + 7z = 6(-3 + z) + 14 -39 + 7z = (-3 * 6 + z * 6) + 14 -39 + 7z = (-18 + 6z) + 14 Reorder the terms: -39 + 7z = -18 + 14 + 6z Combine like terms: -18 + 14 = -4 -39 + 7z = -4 + 6z Solving -39 + 7z = -4 + 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. -39 + 7z + -6z = -4 + 6z + -6z Combine like terms: 7z + -6z = 1z -39 + 1z = -4 + 6z + -6z Combine like terms: 6z + -6z = 0 -39 + 1z = -4 + 0 -39 + 1z = -4 Add '39' to each side of the equation. -39 + 39 + 1z = -4 + 39 Combine like terms: -39 + 39 = 0 0 + 1z = -4 + 39 1z = -4 + 39 Combine like terms: -4 + 39 = 35 1z = 35 Divide each side by '1'. z = 35 Simplifying z = 35
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