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Simplifying (8z + -1)(-20z + 5) = (-80z + -5)(2z + 3) + -5 + 6z Reorder the terms: (-1 + 8z)(-20z + 5) = (-80z + -5)(2z + 3) + -5 + 6z Reorder the terms: (-1 + 8z)(5 + -20z) = (-80z + -5)(2z + 3) + -5 + 6z Multiply (-1 + 8z) * (5 + -20z) (-1(5 + -20z) + 8z * (5 + -20z)) = (-80z + -5)(2z + 3) + -5 + 6z ((5 * -1 + -20z * -1) + 8z * (5 + -20z)) = (-80z + -5)(2z + 3) + -5 + 6z ((-5 + 20z) + 8z * (5 + -20z)) = (-80z + -5)(2z + 3) + -5 + 6z (-5 + 20z + (5 * 8z + -20z * 8z)) = (-80z + -5)(2z + 3) + -5 + 6z (-5 + 20z + (40z + -160z2)) = (-80z + -5)(2z + 3) + -5 + 6z Combine like terms: 20z + 40z = 60z (-5 + 60z + -160z2) = (-80z + -5)(2z + 3) + -5 + 6z Reorder the terms: -5 + 60z + -160z2 = (-5 + -80z)(2z + 3) + -5 + 6z Reorder the terms: -5 + 60z + -160z2 = (-5 + -80z)(3 + 2z) + -5 + 6z Multiply (-5 + -80z) * (3 + 2z) -5 + 60z + -160z2 = (-5(3 + 2z) + -80z * (3 + 2z)) + -5 + 6z -5 + 60z + -160z2 = ((3 * -5 + 2z * -5) + -80z * (3 + 2z)) + -5 + 6z -5 + 60z + -160z2 = ((-15 + -10z) + -80z * (3 + 2z)) + -5 + 6z -5 + 60z + -160z2 = (-15 + -10z + (3 * -80z + 2z * -80z)) + -5 + 6z -5 + 60z + -160z2 = (-15 + -10z + (-240z + -160z2)) + -5 + 6z Combine like terms: -10z + -240z = -250z -5 + 60z + -160z2 = (-15 + -250z + -160z2) + -5 + 6z Reorder the terms: -5 + 60z + -160z2 = -15 + -5 + -250z + 6z + -160z2 Combine like terms: -15 + -5 = -20 -5 + 60z + -160z2 = -20 + -250z + 6z + -160z2 Combine like terms: -250z + 6z = -244z -5 + 60z + -160z2 = -20 + -244z + -160z2 Add '160z2' to each side of the equation. -5 + 60z + -160z2 + 160z2 = -20 + -244z + -160z2 + 160z2 Combine like terms: -160z2 + 160z2 = 0 -5 + 60z + 0 = -20 + -244z + -160z2 + 160z2 -5 + 60z = -20 + -244z + -160z2 + 160z2 Combine like terms: -160z2 + 160z2 = 0 -5 + 60z = -20 + -244z + 0 -5 + 60z = -20 + -244z Solving -5 + 60z = -20 + -244z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '244z' to each side of the equation. -5 + 60z + 244z = -20 + -244z + 244z Combine like terms: 60z + 244z = 304z -5 + 304z = -20 + -244z + 244z Combine like terms: -244z + 244z = 0 -5 + 304z = -20 + 0 -5 + 304z = -20 Add '5' to each side of the equation. -5 + 5 + 304z = -20 + 5 Combine like terms: -5 + 5 = 0 0 + 304z = -20 + 5 304z = -20 + 5 Combine like terms: -20 + 5 = -15 304z = -15 Divide each side by '304'. z = -0.04934210526 Simplifying z = -0.04934210526
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