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Simplifying (8z + -3)(z + 4) + -1(8z + -3)(z + -3) = 0 Reorder the terms: (-3 + 8z)(z + 4) + -1(8z + -3)(z + -3) = 0 Reorder the terms: (-3 + 8z)(4 + z) + -1(8z + -3)(z + -3) = 0 Multiply (-3 + 8z) * (4 + z) (-3(4 + z) + 8z * (4 + z)) + -1(8z + -3)(z + -3) = 0 ((4 * -3 + z * -3) + 8z * (4 + z)) + -1(8z + -3)(z + -3) = 0 ((-12 + -3z) + 8z * (4 + z)) + -1(8z + -3)(z + -3) = 0 (-12 + -3z + (4 * 8z + z * 8z)) + -1(8z + -3)(z + -3) = 0 (-12 + -3z + (32z + 8z2)) + -1(8z + -3)(z + -3) = 0 Combine like terms: -3z + 32z = 29z (-12 + 29z + 8z2) + -1(8z + -3)(z + -3) = 0 Reorder the terms: -12 + 29z + 8z2 + -1(-3 + 8z)(z + -3) = 0 Reorder the terms: -12 + 29z + 8z2 + -1(-3 + 8z)(-3 + z) = 0 Multiply (-3 + 8z) * (-3 + z) -12 + 29z + 8z2 + -1(-3(-3 + z) + 8z * (-3 + z)) = 0 -12 + 29z + 8z2 + -1((-3 * -3 + z * -3) + 8z * (-3 + z)) = 0 -12 + 29z + 8z2 + -1((9 + -3z) + 8z * (-3 + z)) = 0 -12 + 29z + 8z2 + -1(9 + -3z + (-3 * 8z + z * 8z)) = 0 -12 + 29z + 8z2 + -1(9 + -3z + (-24z + 8z2)) = 0 Combine like terms: -3z + -24z = -27z -12 + 29z + 8z2 + -1(9 + -27z + 8z2) = 0 -12 + 29z + 8z2 + (9 * -1 + -27z * -1 + 8z2 * -1) = 0 -12 + 29z + 8z2 + (-9 + 27z + -8z2) = 0 Reorder the terms: -12 + -9 + 29z + 27z + 8z2 + -8z2 = 0 Combine like terms: -12 + -9 = -21 -21 + 29z + 27z + 8z2 + -8z2 = 0 Combine like terms: 29z + 27z = 56z -21 + 56z + 8z2 + -8z2 = 0 Combine like terms: 8z2 + -8z2 = 0 -21 + 56z + 0 = 0 -21 + 56z = 0 Solving -21 + 56z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + 56z = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 56z = 0 + 21 56z = 0 + 21 Combine like terms: 0 + 21 = 21 56z = 21 Divide each side by '56'. z = 0.375 Simplifying z = 0.375
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