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Simplifying 5(3z + 13) = 6(5z + 3) Reorder the terms: 5(13 + 3z) = 6(5z + 3) (13 * 5 + 3z * 5) = 6(5z + 3) (65 + 15z) = 6(5z + 3) Reorder the terms: 65 + 15z = 6(3 + 5z) 65 + 15z = (3 * 6 + 5z * 6) 65 + 15z = (18 + 30z) Solving 65 + 15z = 18 + 30z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-30z' to each side of the equation. 65 + 15z + -30z = 18 + 30z + -30z Combine like terms: 15z + -30z = -15z 65 + -15z = 18 + 30z + -30z Combine like terms: 30z + -30z = 0 65 + -15z = 18 + 0 65 + -15z = 18 Add '-65' to each side of the equation. 65 + -65 + -15z = 18 + -65 Combine like terms: 65 + -65 = 0 0 + -15z = 18 + -65 -15z = 18 + -65 Combine like terms: 18 + -65 = -47 -15z = -47 Divide each side by '-15'. z = 3.133333333 Simplifying z = 3.133333333
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