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Simplifying 5(4z + -1) + -5(z + 4) = 12(z + 1) Reorder the terms: 5(-1 + 4z) + -5(z + 4) = 12(z + 1) (-1 * 5 + 4z * 5) + -5(z + 4) = 12(z + 1) (-5 + 20z) + -5(z + 4) = 12(z + 1) Reorder the terms: -5 + 20z + -5(4 + z) = 12(z + 1) -5 + 20z + (4 * -5 + z * -5) = 12(z + 1) -5 + 20z + (-20 + -5z) = 12(z + 1) Reorder the terms: -5 + -20 + 20z + -5z = 12(z + 1) Combine like terms: -5 + -20 = -25 -25 + 20z + -5z = 12(z + 1) Combine like terms: 20z + -5z = 15z -25 + 15z = 12(z + 1) Reorder the terms: -25 + 15z = 12(1 + z) -25 + 15z = (1 * 12 + z * 12) -25 + 15z = (12 + 12z) Solving -25 + 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. -25 + 15z + -12z = 12 + 12z + -12z Combine like terms: 15z + -12z = 3z -25 + 3z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -25 + 3z = 12 + 0 -25 + 3z = 12 Add '25' to each side of the equation. -25 + 25 + 3z = 12 + 25 Combine like terms: -25 + 25 = 0 0 + 3z = 12 + 25 3z = 12 + 25 Combine like terms: 12 + 25 = 37 3z = 37 Divide each side by '3'. z = 12.33333333 Simplifying z = 12.33333333
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