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Simplifying 12(z + 4) + -3(z + -2) = 4(z + -1) + 4(z + -4) Reorder the terms: 12(4 + z) + -3(z + -2) = 4(z + -1) + 4(z + -4) (4 * 12 + z * 12) + -3(z + -2) = 4(z + -1) + 4(z + -4) (48 + 12z) + -3(z + -2) = 4(z + -1) + 4(z + -4) Reorder the terms: 48 + 12z + -3(-2 + z) = 4(z + -1) + 4(z + -4) 48 + 12z + (-2 * -3 + z * -3) = 4(z + -1) + 4(z + -4) 48 + 12z + (6 + -3z) = 4(z + -1) + 4(z + -4) Reorder the terms: 48 + 6 + 12z + -3z = 4(z + -1) + 4(z + -4) Combine like terms: 48 + 6 = 54 54 + 12z + -3z = 4(z + -1) + 4(z + -4) Combine like terms: 12z + -3z = 9z 54 + 9z = 4(z + -1) + 4(z + -4) Reorder the terms: 54 + 9z = 4(-1 + z) + 4(z + -4) 54 + 9z = (-1 * 4 + z * 4) + 4(z + -4) 54 + 9z = (-4 + 4z) + 4(z + -4) Reorder the terms: 54 + 9z = -4 + 4z + 4(-4 + z) 54 + 9z = -4 + 4z + (-4 * 4 + z * 4) 54 + 9z = -4 + 4z + (-16 + 4z) Reorder the terms: 54 + 9z = -4 + -16 + 4z + 4z Combine like terms: -4 + -16 = -20 54 + 9z = -20 + 4z + 4z Combine like terms: 4z + 4z = 8z 54 + 9z = -20 + 8z Solving 54 + 9z = -20 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. 54 + 9z + -8z = -20 + 8z + -8z Combine like terms: 9z + -8z = 1z 54 + 1z = -20 + 8z + -8z Combine like terms: 8z + -8z = 0 54 + 1z = -20 + 0 54 + 1z = -20 Add '-54' to each side of the equation. 54 + -54 + 1z = -20 + -54 Combine like terms: 54 + -54 = 0 0 + 1z = -20 + -54 1z = -20 + -54 Combine like terms: -20 + -54 = -74 1z = -74 Divide each side by '1'. z = -74 Simplifying z = -74
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