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Simplifying (8z + -3)(z + 9) + -1(8z + -3)(z + -8) = 0 Reorder the terms: (-3 + 8z)(z + 9) + -1(8z + -3)(z + -8) = 0 Reorder the terms: (-3 + 8z)(9 + z) + -1(8z + -3)(z + -8) = 0 Multiply (-3 + 8z) * (9 + z) (-3(9 + z) + 8z * (9 + z)) + -1(8z + -3)(z + -8) = 0 ((9 * -3 + z * -3) + 8z * (9 + z)) + -1(8z + -3)(z + -8) = 0 ((-27 + -3z) + 8z * (9 + z)) + -1(8z + -3)(z + -8) = 0 (-27 + -3z + (9 * 8z + z * 8z)) + -1(8z + -3)(z + -8) = 0 (-27 + -3z + (72z + 8z2)) + -1(8z + -3)(z + -8) = 0 Combine like terms: -3z + 72z = 69z (-27 + 69z + 8z2) + -1(8z + -3)(z + -8) = 0 Reorder the terms: -27 + 69z + 8z2 + -1(-3 + 8z)(z + -8) = 0 Reorder the terms: -27 + 69z + 8z2 + -1(-3 + 8z)(-8 + z) = 0 Multiply (-3 + 8z) * (-8 + z) -27 + 69z + 8z2 + -1(-3(-8 + z) + 8z * (-8 + z)) = 0 -27 + 69z + 8z2 + -1((-8 * -3 + z * -3) + 8z * (-8 + z)) = 0 -27 + 69z + 8z2 + -1((24 + -3z) + 8z * (-8 + z)) = 0 -27 + 69z + 8z2 + -1(24 + -3z + (-8 * 8z + z * 8z)) = 0 -27 + 69z + 8z2 + -1(24 + -3z + (-64z + 8z2)) = 0 Combine like terms: -3z + -64z = -67z -27 + 69z + 8z2 + -1(24 + -67z + 8z2) = 0 -27 + 69z + 8z2 + (24 * -1 + -67z * -1 + 8z2 * -1) = 0 -27 + 69z + 8z2 + (-24 + 67z + -8z2) = 0 Reorder the terms: -27 + -24 + 69z + 67z + 8z2 + -8z2 = 0 Combine like terms: -27 + -24 = -51 -51 + 69z + 67z + 8z2 + -8z2 = 0 Combine like terms: 69z + 67z = 136z -51 + 136z + 8z2 + -8z2 = 0 Combine like terms: 8z2 + -8z2 = 0 -51 + 136z + 0 = 0 -51 + 136z = 0 Solving -51 + 136z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + 136z = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 136z = 0 + 51 136z = 0 + 51 Combine like terms: 0 + 51 = 51 136z = 51 Divide each side by '136'. z = 0.375 Simplifying z = 0.375
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