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Simplifying -20(z + 3) + 6(4z + -3) = 3(z + -6) + 14 Reorder the terms: -20(3 + z) + 6(4z + -3) = 3(z + -6) + 14 (3 * -20 + z * -20) + 6(4z + -3) = 3(z + -6) + 14 (-60 + -20z) + 6(4z + -3) = 3(z + -6) + 14 Reorder the terms: -60 + -20z + 6(-3 + 4z) = 3(z + -6) + 14 -60 + -20z + (-3 * 6 + 4z * 6) = 3(z + -6) + 14 -60 + -20z + (-18 + 24z) = 3(z + -6) + 14 Reorder the terms: -60 + -18 + -20z + 24z = 3(z + -6) + 14 Combine like terms: -60 + -18 = -78 -78 + -20z + 24z = 3(z + -6) + 14 Combine like terms: -20z + 24z = 4z -78 + 4z = 3(z + -6) + 14 Reorder the terms: -78 + 4z = 3(-6 + z) + 14 -78 + 4z = (-6 * 3 + z * 3) + 14 -78 + 4z = (-18 + 3z) + 14 Reorder the terms: -78 + 4z = -18 + 14 + 3z Combine like terms: -18 + 14 = -4 -78 + 4z = -4 + 3z Solving -78 + 4z = -4 + 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. -78 + 4z + -3z = -4 + 3z + -3z Combine like terms: 4z + -3z = 1z -78 + 1z = -4 + 3z + -3z Combine like terms: 3z + -3z = 0 -78 + 1z = -4 + 0 -78 + 1z = -4 Add '78' to each side of the equation. -78 + 78 + 1z = -4 + 78 Combine like terms: -78 + 78 = 0 0 + 1z = -4 + 78 1z = -4 + 78 Combine like terms: -4 + 78 = 74 1z = 74 Divide each side by '1'. z = 74 Simplifying z = 74
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