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Simplifying 2[(3z + -2) + 6z] = 13(z + 1) + 29 Reorder the terms: 2[(-2 + 3z) + 6z] = 13(z + 1) + 29 Remove parenthesis around (-2 + 3z) 2[-2 + 3z + 6z] = 13(z + 1) + 29 Combine like terms: 3z + 6z = 9z 2[-2 + 9z] = 13(z + 1) + 29 [-2 * 2 + 9z * 2] = 13(z + 1) + 29 [-4 + 18z] = 13(z + 1) + 29 Reorder the terms: -4 + 18z = 13(1 + z) + 29 -4 + 18z = (1 * 13 + z * 13) + 29 -4 + 18z = (13 + 13z) + 29 Reorder the terms: -4 + 18z = 13 + 29 + 13z Combine like terms: 13 + 29 = 42 -4 + 18z = 42 + 13z Solving -4 + 18z = 42 + 13z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-13z' to each side of the equation. -4 + 18z + -13z = 42 + 13z + -13z Combine like terms: 18z + -13z = 5z -4 + 5z = 42 + 13z + -13z Combine like terms: 13z + -13z = 0 -4 + 5z = 42 + 0 -4 + 5z = 42 Add '4' to each side of the equation. -4 + 4 + 5z = 42 + 4 Combine like terms: -4 + 4 = 0 0 + 5z = 42 + 4 5z = 42 + 4 Combine like terms: 42 + 4 = 46 5z = 46 Divide each side by '5'. z = 9.2 Simplifying z = 9.2
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