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Simplifying -14(z + 1) + 6(3z + -5) = 3(z + -5) + 12 Reorder the terms: -14(1 + z) + 6(3z + -5) = 3(z + -5) + 12 (1 * -14 + z * -14) + 6(3z + -5) = 3(z + -5) + 12 (-14 + -14z) + 6(3z + -5) = 3(z + -5) + 12 Reorder the terms: -14 + -14z + 6(-5 + 3z) = 3(z + -5) + 12 -14 + -14z + (-5 * 6 + 3z * 6) = 3(z + -5) + 12 -14 + -14z + (-30 + 18z) = 3(z + -5) + 12 Reorder the terms: -14 + -30 + -14z + 18z = 3(z + -5) + 12 Combine like terms: -14 + -30 = -44 -44 + -14z + 18z = 3(z + -5) + 12 Combine like terms: -14z + 18z = 4z -44 + 4z = 3(z + -5) + 12 Reorder the terms: -44 + 4z = 3(-5 + z) + 12 -44 + 4z = (-5 * 3 + z * 3) + 12 -44 + 4z = (-15 + 3z) + 12 Reorder the terms: -44 + 4z = -15 + 12 + 3z Combine like terms: -15 + 12 = -3 -44 + 4z = -3 + 3z Solving -44 + 4z = -3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -44 + 4z + -3z = -3 + 3z + -3z Combine like terms: 4z + -3z = 1z -44 + 1z = -3 + 3z + -3z Combine like terms: 3z + -3z = 0 -44 + 1z = -3 + 0 -44 + 1z = -3 Add '44' to each side of the equation. -44 + 44 + 1z = -3 + 44 Combine like terms: -44 + 44 = 0 0 + 1z = -3 + 44 1z = -3 + 44 Combine like terms: -3 + 44 = 41 1z = 41 Divide each side by '1'. z = 41 Simplifying z = 41
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