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Simplifying (2z + 1)(2z + -1) = -4z2 + -5z + 2 Reorder the terms: (1 + 2z)(2z + -1) = -4z2 + -5z + 2 Reorder the terms: (1 + 2z)(-1 + 2z) = -4z2 + -5z + 2 Multiply (1 + 2z) * (-1 + 2z) (1(-1 + 2z) + 2z * (-1 + 2z)) = -4z2 + -5z + 2 ((-1 * 1 + 2z * 1) + 2z * (-1 + 2z)) = -4z2 + -5z + 2 ((-1 + 2z) + 2z * (-1 + 2z)) = -4z2 + -5z + 2 (-1 + 2z + (-1 * 2z + 2z * 2z)) = -4z2 + -5z + 2 (-1 + 2z + (-2z + 4z2)) = -4z2 + -5z + 2 Combine like terms: 2z + -2z = 0 (-1 + 0 + 4z2) = -4z2 + -5z + 2 (-1 + 4z2) = -4z2 + -5z + 2 Reorder the terms: -1 + 4z2 = 2 + -5z + -4z2 Solving -1 + 4z2 = 2 + -5z + -4z2 Solving for variable 'z'. Reorder the terms: -1 + -2 + 5z + 4z2 + 4z2 = 2 + -5z + -4z2 + -2 + 5z + 4z2 Combine like terms: -1 + -2 = -3 -3 + 5z + 4z2 + 4z2 = 2 + -5z + -4z2 + -2 + 5z + 4z2 Combine like terms: 4z2 + 4z2 = 8z2 -3 + 5z + 8z2 = 2 + -5z + -4z2 + -2 + 5z + 4z2 Reorder the terms: -3 + 5z + 8z2 = 2 + -2 + -5z + 5z + -4z2 + 4z2 Combine like terms: 2 + -2 = 0 -3 + 5z + 8z2 = 0 + -5z + 5z + -4z2 + 4z2 -3 + 5z + 8z2 = -5z + 5z + -4z2 + 4z2 Combine like terms: -5z + 5z = 0 -3 + 5z + 8z2 = 0 + -4z2 + 4z2 -3 + 5z + 8z2 = -4z2 + 4z2 Combine like terms: -4z2 + 4z2 = 0 -3 + 5z + 8z2 = 0 Factor a trinomial. (-1 + -1z)(3 + -8z) = 0Subproblem 1
Set the factor '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1Subproblem 2
Set the factor '(3 + -8z)' equal to zero and attempt to solve: Simplifying 3 + -8z = 0 Solving 3 + -8z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8z = 0 + -3 -8z = 0 + -3 Combine like terms: 0 + -3 = -3 -8z = -3 Divide each side by '-8'. z = 0.375 Simplifying z = 0.375Solution
z = {-1, 0.375}
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