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Simplifying -1(2(3z + -3) + -1(1 + z)) + -1(5(3 + -2z) + -1(1 + 2)) = 0 Reorder the terms: -1(2(-3 + 3z) + -1(1 + z)) + -1(5(3 + -2z) + -1(1 + 2)) = 0 -1((-3 * 2 + 3z * 2) + -1(1 + z)) + -1(5(3 + -2z) + -1(1 + 2)) = 0 -1((-6 + 6z) + -1(1 + z)) + -1(5(3 + -2z) + -1(1 + 2)) = 0 -1(-6 + 6z + (1 * -1 + z * -1)) + -1(5(3 + -2z) + -1(1 + 2)) = 0 -1(-6 + 6z + (-1 + -1z)) + -1(5(3 + -2z) + -1(1 + 2)) = 0 Reorder the terms: -1(-6 + -1 + 6z + -1z) + -1(5(3 + -2z) + -1(1 + 2)) = 0 Combine like terms: -6 + -1 = -7 -1(-7 + 6z + -1z) + -1(5(3 + -2z) + -1(1 + 2)) = 0 Combine like terms: 6z + -1z = 5z -1(-7 + 5z) + -1(5(3 + -2z) + -1(1 + 2)) = 0 (-7 * -1 + 5z * -1) + -1(5(3 + -2z) + -1(1 + 2)) = 0 (7 + -5z) + -1(5(3 + -2z) + -1(1 + 2)) = 0 7 + -5z + -1((3 * 5 + -2z * 5) + -1(1 + 2)) = 0 7 + -5z + -1((15 + -10z) + -1(1 + 2)) = 0 Combine like terms: 1 + 2 = 3 7 + -5z + -1(15 + -10z + -1(3)) = 0 Multiply -1 * 3 7 + -5z + -1(15 + -10z + -3) = 0 Reorder the terms: 7 + -5z + -1(15 + -3 + -10z) = 0 Combine like terms: 15 + -3 = 12 7 + -5z + -1(12 + -10z) = 0 7 + -5z + (12 * -1 + -10z * -1) = 0 7 + -5z + (-12 + 10z) = 0 Reorder the terms: 7 + -12 + -5z + 10z = 0 Combine like terms: 7 + -12 = -5 -5 + -5z + 10z = 0 Combine like terms: -5z + 10z = 5z -5 + 5z = 0 Solving -5 + 5z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 5z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 5z = 0 + 5 5z = 0 + 5 Combine like terms: 0 + 5 = 5 5z = 5 Divide each side by '5'. z = 1 Simplifying z = 1
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