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Simplifying -3(z + 1) + 3(3z + -6) = 5(z + -4) + 14 Reorder the terms: -3(1 + z) + 3(3z + -6) = 5(z + -4) + 14 (1 * -3 + z * -3) + 3(3z + -6) = 5(z + -4) + 14 (-3 + -3z) + 3(3z + -6) = 5(z + -4) + 14 Reorder the terms: -3 + -3z + 3(-6 + 3z) = 5(z + -4) + 14 -3 + -3z + (-6 * 3 + 3z * 3) = 5(z + -4) + 14 -3 + -3z + (-18 + 9z) = 5(z + -4) + 14 Reorder the terms: -3 + -18 + -3z + 9z = 5(z + -4) + 14 Combine like terms: -3 + -18 = -21 -21 + -3z + 9z = 5(z + -4) + 14 Combine like terms: -3z + 9z = 6z -21 + 6z = 5(z + -4) + 14 Reorder the terms: -21 + 6z = 5(-4 + z) + 14 -21 + 6z = (-4 * 5 + z * 5) + 14 -21 + 6z = (-20 + 5z) + 14 Reorder the terms: -21 + 6z = -20 + 14 + 5z Combine like terms: -20 + 14 = -6 -21 + 6z = -6 + 5z Solving -21 + 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. -21 + 6z + -5z = -6 + 5z + -5z Combine like terms: 6z + -5z = 1z -21 + 1z = -6 + 5z + -5z Combine like terms: 5z + -5z = 0 -21 + 1z = -6 + 0 -21 + 1z = -6 Add '21' to each side of the equation. -21 + 21 + 1z = -6 + 21 Combine like terms: -21 + 21 = 0 0 + 1z = -6 + 21 1z = -6 + 21 Combine like terms: -6 + 21 = 15 1z = 15 Divide each side by '1'. z = 15 Simplifying z = 15
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