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Simplifying 2(4z + 6) + -3(2z + -3) = 4z + -4 + 5 + -1z Reorder the terms: 2(6 + 4z) + -3(2z + -3) = 4z + -4 + 5 + -1z (6 * 2 + 4z * 2) + -3(2z + -3) = 4z + -4 + 5 + -1z (12 + 8z) + -3(2z + -3) = 4z + -4 + 5 + -1z Reorder the terms: 12 + 8z + -3(-3 + 2z) = 4z + -4 + 5 + -1z 12 + 8z + (-3 * -3 + 2z * -3) = 4z + -4 + 5 + -1z 12 + 8z + (9 + -6z) = 4z + -4 + 5 + -1z Reorder the terms: 12 + 9 + 8z + -6z = 4z + -4 + 5 + -1z Combine like terms: 12 + 9 = 21 21 + 8z + -6z = 4z + -4 + 5 + -1z Combine like terms: 8z + -6z = 2z 21 + 2z = 4z + -4 + 5 + -1z Reorder the terms: 21 + 2z = -4 + 5 + 4z + -1z Combine like terms: -4 + 5 = 1 21 + 2z = 1 + 4z + -1z Combine like terms: 4z + -1z = 3z 21 + 2z = 1 + 3z Solving 21 + 2z = 1 + 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. 21 + 2z + -3z = 1 + 3z + -3z Combine like terms: 2z + -3z = -1z 21 + -1z = 1 + 3z + -3z Combine like terms: 3z + -3z = 0 21 + -1z = 1 + 0 21 + -1z = 1 Add '-21' to each side of the equation. 21 + -21 + -1z = 1 + -21 Combine like terms: 21 + -21 = 0 0 + -1z = 1 + -21 -1z = 1 + -21 Combine like terms: 1 + -21 = -20 -1z = -20 Divide each side by '-1'. z = 20 Simplifying z = 20
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