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Simplifying -6(z + 3) + 3(4z + -5) = 5(z + -4) + 14 Reorder the terms: -6(3 + z) + 3(4z + -5) = 5(z + -4) + 14 (3 * -6 + z * -6) + 3(4z + -5) = 5(z + -4) + 14 (-18 + -6z) + 3(4z + -5) = 5(z + -4) + 14 Reorder the terms: -18 + -6z + 3(-5 + 4z) = 5(z + -4) + 14 -18 + -6z + (-5 * 3 + 4z * 3) = 5(z + -4) + 14 -18 + -6z + (-15 + 12z) = 5(z + -4) + 14 Reorder the terms: -18 + -15 + -6z + 12z = 5(z + -4) + 14 Combine like terms: -18 + -15 = -33 -33 + -6z + 12z = 5(z + -4) + 14 Combine like terms: -6z + 12z = 6z -33 + 6z = 5(z + -4) + 14 Reorder the terms: -33 + 6z = 5(-4 + z) + 14 -33 + 6z = (-4 * 5 + z * 5) + 14 -33 + 6z = (-20 + 5z) + 14 Reorder the terms: -33 + 6z = -20 + 14 + 5z Combine like terms: -20 + 14 = -6 -33 + 6z = -6 + 5z Solving -33 + 6z = -6 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -33 + 6z + -5z = -6 + 5z + -5z Combine like terms: 6z + -5z = 1z -33 + 1z = -6 + 5z + -5z Combine like terms: 5z + -5z = 0 -33 + 1z = -6 + 0 -33 + 1z = -6 Add '33' to each side of the equation. -33 + 33 + 1z = -6 + 33 Combine like terms: -33 + 33 = 0 0 + 1z = -6 + 33 1z = -6 + 33 Combine like terms: -6 + 33 = 27 1z = 27 Divide each side by '1'. z = 27 Simplifying z = 27
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