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Simplifying 4(5z + -1) + -5(z + 6) = 12(z + 1) Reorder the terms: 4(-1 + 5z) + -5(z + 6) = 12(z + 1) (-1 * 4 + 5z * 4) + -5(z + 6) = 12(z + 1) (-4 + 20z) + -5(z + 6) = 12(z + 1) Reorder the terms: -4 + 20z + -5(6 + z) = 12(z + 1) -4 + 20z + (6 * -5 + z * -5) = 12(z + 1) -4 + 20z + (-30 + -5z) = 12(z + 1) Reorder the terms: -4 + -30 + 20z + -5z = 12(z + 1) Combine like terms: -4 + -30 = -34 -34 + 20z + -5z = 12(z + 1) Combine like terms: 20z + -5z = 15z -34 + 15z = 12(z + 1) Reorder the terms: -34 + 15z = 12(1 + z) -34 + 15z = (1 * 12 + z * 12) -34 + 15z = (12 + 12z) Solving -34 + 15z = 12 + 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. -34 + 15z + -12z = 12 + 12z + -12z Combine like terms: 15z + -12z = 3z -34 + 3z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -34 + 3z = 12 + 0 -34 + 3z = 12 Add '34' to each side of the equation. -34 + 34 + 3z = 12 + 34 Combine like terms: -34 + 34 = 0 0 + 3z = 12 + 34 3z = 12 + 34 Combine like terms: 12 + 34 = 46 3z = 46 Divide each side by '3'. z = 15.33333333 Simplifying z = 15.33333333
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