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Simplifying -5(z + 3) + 3(4z + -6) = 6(z + -6) + 14 Reorder the terms: -5(3 + z) + 3(4z + -6) = 6(z + -6) + 14 (3 * -5 + z * -5) + 3(4z + -6) = 6(z + -6) + 14 (-15 + -5z) + 3(4z + -6) = 6(z + -6) + 14 Reorder the terms: -15 + -5z + 3(-6 + 4z) = 6(z + -6) + 14 -15 + -5z + (-6 * 3 + 4z * 3) = 6(z + -6) + 14 -15 + -5z + (-18 + 12z) = 6(z + -6) + 14 Reorder the terms: -15 + -18 + -5z + 12z = 6(z + -6) + 14 Combine like terms: -15 + -18 = -33 -33 + -5z + 12z = 6(z + -6) + 14 Combine like terms: -5z + 12z = 7z -33 + 7z = 6(z + -6) + 14 Reorder the terms: -33 + 7z = 6(-6 + z) + 14 -33 + 7z = (-6 * 6 + z * 6) + 14 -33 + 7z = (-36 + 6z) + 14 Reorder the terms: -33 + 7z = -36 + 14 + 6z Combine like terms: -36 + 14 = -22 -33 + 7z = -22 + 6z Solving -33 + 7z = -22 + 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. -33 + 7z + -6z = -22 + 6z + -6z Combine like terms: 7z + -6z = 1z -33 + 1z = -22 + 6z + -6z Combine like terms: 6z + -6z = 0 -33 + 1z = -22 + 0 -33 + 1z = -22 Add '33' to each side of the equation. -33 + 33 + 1z = -22 + 33 Combine like terms: -33 + 33 = 0 0 + 1z = -22 + 33 1z = -22 + 33 Combine like terms: -22 + 33 = 11 1z = 11 Divide each side by '1'. z = 11 Simplifying z = 11
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