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Simplifying 7(z + -1) + -1(-6z + -8) = 12z Reorder the terms: 7(-1 + z) + -1(-6z + -8) = 12z (-1 * 7 + z * 7) + -1(-6z + -8) = 12z (-7 + 7z) + -1(-6z + -8) = 12z Reorder the terms: -7 + 7z + -1(-8 + -6z) = 12z -7 + 7z + (-8 * -1 + -6z * -1) = 12z -7 + 7z + (8 + 6z) = 12z Reorder the terms: -7 + 8 + 7z + 6z = 12z Combine like terms: -7 + 8 = 1 1 + 7z + 6z = 12z Combine like terms: 7z + 6z = 13z 1 + 13z = 12z Solving 1 + 13z = 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. 1 + 13z + -12z = 12z + -12z Combine like terms: 13z + -12z = 1z 1 + 1z = 12z + -12z Combine like terms: 12z + -12z = 0 1 + 1z = 0 Add '-1' to each side of the equation. 1 + -1 + 1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1z = 0 + -1 1z = 0 + -1 Combine like terms: 0 + -1 = -1 1z = -1 Divide each side by '1'. z = -1 Simplifying z = -1
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