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Simplifying -9(z + 3) + 5(3z + -3) = 5(z + -3) + 9 Reorder the terms: -9(3 + z) + 5(3z + -3) = 5(z + -3) + 9 (3 * -9 + z * -9) + 5(3z + -3) = 5(z + -3) + 9 (-27 + -9z) + 5(3z + -3) = 5(z + -3) + 9 Reorder the terms: -27 + -9z + 5(-3 + 3z) = 5(z + -3) + 9 -27 + -9z + (-3 * 5 + 3z * 5) = 5(z + -3) + 9 -27 + -9z + (-15 + 15z) = 5(z + -3) + 9 Reorder the terms: -27 + -15 + -9z + 15z = 5(z + -3) + 9 Combine like terms: -27 + -15 = -42 -42 + -9z + 15z = 5(z + -3) + 9 Combine like terms: -9z + 15z = 6z -42 + 6z = 5(z + -3) + 9 Reorder the terms: -42 + 6z = 5(-3 + z) + 9 -42 + 6z = (-3 * 5 + z * 5) + 9 -42 + 6z = (-15 + 5z) + 9 Reorder the terms: -42 + 6z = -15 + 9 + 5z Combine like terms: -15 + 9 = -6 -42 + 6z = -6 + 5z Solving -42 + 6z = -6 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -42 + 6z + -5z = -6 + 5z + -5z Combine like terms: 6z + -5z = 1z -42 + 1z = -6 + 5z + -5z Combine like terms: 5z + -5z = 0 -42 + 1z = -6 + 0 -42 + 1z = -6 Add '42' to each side of the equation. -42 + 42 + 1z = -6 + 42 Combine like terms: -42 + 42 = 0 0 + 1z = -6 + 42 1z = -6 + 42 Combine like terms: -6 + 42 = 36 1z = 36 Divide each side by '1'. z = 36 Simplifying z = 36
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