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Simplifying -1(2(3z + -3) + -1(1 + -1z)) + -1(5(3 + -2z) + -1(1 + z)) = 0 Reorder the terms: -1(2(-3 + 3z) + -1(1 + -1z)) + -1(5(3 + -2z) + -1(1 + z)) = 0 -1((-3 * 2 + 3z * 2) + -1(1 + -1z)) + -1(5(3 + -2z) + -1(1 + z)) = 0 -1((-6 + 6z) + -1(1 + -1z)) + -1(5(3 + -2z) + -1(1 + z)) = 0 -1(-6 + 6z + (1 * -1 + -1z * -1)) + -1(5(3 + -2z) + -1(1 + z)) = 0 -1(-6 + 6z + (-1 + 1z)) + -1(5(3 + -2z) + -1(1 + z)) = 0 Reorder the terms: -1(-6 + -1 + 6z + 1z) + -1(5(3 + -2z) + -1(1 + z)) = 0 Combine like terms: -6 + -1 = -7 -1(-7 + 6z + 1z) + -1(5(3 + -2z) + -1(1 + z)) = 0 Combine like terms: 6z + 1z = 7z -1(-7 + 7z) + -1(5(3 + -2z) + -1(1 + z)) = 0 (-7 * -1 + 7z * -1) + -1(5(3 + -2z) + -1(1 + z)) = 0 (7 + -7z) + -1(5(3 + -2z) + -1(1 + z)) = 0 7 + -7z + -1((3 * 5 + -2z * 5) + -1(1 + z)) = 0 7 + -7z + -1((15 + -10z) + -1(1 + z)) = 0 7 + -7z + -1(15 + -10z + (1 * -1 + z * -1)) = 0 7 + -7z + -1(15 + -10z + (-1 + -1z)) = 0 Reorder the terms: 7 + -7z + -1(15 + -1 + -10z + -1z) = 0 Combine like terms: 15 + -1 = 14 7 + -7z + -1(14 + -10z + -1z) = 0 Combine like terms: -10z + -1z = -11z 7 + -7z + -1(14 + -11z) = 0 7 + -7z + (14 * -1 + -11z * -1) = 0 7 + -7z + (-14 + 11z) = 0 Reorder the terms: 7 + -14 + -7z + 11z = 0 Combine like terms: 7 + -14 = -7 -7 + -7z + 11z = 0 Combine like terms: -7z + 11z = 4z -7 + 4z = 0 Solving -7 + 4z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 4z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4z = 0 + 7 4z = 0 + 7 Combine like terms: 0 + 7 = 7 4z = 7 Divide each side by '4'. z = 1.75 Simplifying z = 1.75
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