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Simplifying 3(4z + 9) + -4(z + 9) = 0 Reorder the terms: 3(9 + 4z) + -4(z + 9) = 0 (9 * 3 + 4z * 3) + -4(z + 9) = 0 (27 + 12z) + -4(z + 9) = 0 Reorder the terms: 27 + 12z + -4(9 + z) = 0 27 + 12z + (9 * -4 + z * -4) = 0 27 + 12z + (-36 + -4z) = 0 Reorder the terms: 27 + -36 + 12z + -4z = 0 Combine like terms: 27 + -36 = -9 -9 + 12z + -4z = 0 Combine like terms: 12z + -4z = 8z -9 + 8z = 0 Solving -9 + 8z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 8z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 8z = 0 + 9 8z = 0 + 9 Combine like terms: 0 + 9 = 9 8z = 9 Divide each side by '8'. z = 1.125 Simplifying z = 1.125
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