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Simplifying (8z + -3)(z + 5) + -1(8z + -3)(z + -4) = 0 Reorder the terms: (-3 + 8z)(z + 5) + -1(8z + -3)(z + -4) = 0 Reorder the terms: (-3 + 8z)(5 + z) + -1(8z + -3)(z + -4) = 0 Multiply (-3 + 8z) * (5 + z) (-3(5 + z) + 8z * (5 + z)) + -1(8z + -3)(z + -4) = 0 ((5 * -3 + z * -3) + 8z * (5 + z)) + -1(8z + -3)(z + -4) = 0 ((-15 + -3z) + 8z * (5 + z)) + -1(8z + -3)(z + -4) = 0 (-15 + -3z + (5 * 8z + z * 8z)) + -1(8z + -3)(z + -4) = 0 (-15 + -3z + (40z + 8z2)) + -1(8z + -3)(z + -4) = 0 Combine like terms: -3z + 40z = 37z (-15 + 37z + 8z2) + -1(8z + -3)(z + -4) = 0 Reorder the terms: -15 + 37z + 8z2 + -1(-3 + 8z)(z + -4) = 0 Reorder the terms: -15 + 37z + 8z2 + -1(-3 + 8z)(-4 + z) = 0 Multiply (-3 + 8z) * (-4 + z) -15 + 37z + 8z2 + -1(-3(-4 + z) + 8z * (-4 + z)) = 0 -15 + 37z + 8z2 + -1((-4 * -3 + z * -3) + 8z * (-4 + z)) = 0 -15 + 37z + 8z2 + -1((12 + -3z) + 8z * (-4 + z)) = 0 -15 + 37z + 8z2 + -1(12 + -3z + (-4 * 8z + z * 8z)) = 0 -15 + 37z + 8z2 + -1(12 + -3z + (-32z + 8z2)) = 0 Combine like terms: -3z + -32z = -35z -15 + 37z + 8z2 + -1(12 + -35z + 8z2) = 0 -15 + 37z + 8z2 + (12 * -1 + -35z * -1 + 8z2 * -1) = 0 -15 + 37z + 8z2 + (-12 + 35z + -8z2) = 0 Reorder the terms: -15 + -12 + 37z + 35z + 8z2 + -8z2 = 0 Combine like terms: -15 + -12 = -27 -27 + 37z + 35z + 8z2 + -8z2 = 0 Combine like terms: 37z + 35z = 72z -27 + 72z + 8z2 + -8z2 = 0 Combine like terms: 8z2 + -8z2 = 0 -27 + 72z + 0 = 0 -27 + 72z = 0 Solving -27 + 72z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + 72z = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 72z = 0 + 27 72z = 0 + 27 Combine like terms: 0 + 27 = 27 72z = 27 Divide each side by '72'. z = 0.375 Simplifying z = 0.375
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