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Simplifying z + -6 + -7(z + -5) + 5(6z + 1) = 0 Reorder the terms: z + -6 + -7(-5 + z) + 5(6z + 1) = 0 z + -6 + (-5 * -7 + z * -7) + 5(6z + 1) = 0 z + -6 + (35 + -7z) + 5(6z + 1) = 0 Reorder the terms: z + -6 + 35 + -7z + 5(1 + 6z) = 0 z + -6 + 35 + -7z + (1 * 5 + 6z * 5) = 0 z + -6 + 35 + -7z + (5 + 30z) = 0 Reorder the terms: -6 + 35 + 5 + z + -7z + 30z = 0 Combine like terms: -6 + 35 = 29 29 + 5 + z + -7z + 30z = 0 Combine like terms: 29 + 5 = 34 34 + z + -7z + 30z = 0 Combine like terms: z + -7z = -6z 34 + -6z + 30z = 0 Combine like terms: -6z + 30z = 24z 34 + 24z = 0 Solving 34 + 24z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + 24z = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 24z = 0 + -34 24z = 0 + -34 Combine like terms: 0 + -34 = -34 24z = -34 Divide each side by '24'. z = -1.416666667 Simplifying z = -1.416666667
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