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Simplifying 0 = 4z2 + -33z + -27 Reorder the terms: 0 = -27 + -33z + 4z2 Solving 0 = -27 + -33z + 4z2 Solving for variable 'z'. Combine like terms: 0 + 27 = 27 27 + 33z + -4z2 = -27 + -33z + 4z2 + 27 + 33z + -4z2 Reorder the terms: 27 + 33z + -4z2 = -27 + 27 + -33z + 33z + 4z2 + -4z2 Combine like terms: -27 + 27 = 0 27 + 33z + -4z2 = 0 + -33z + 33z + 4z2 + -4z2 27 + 33z + -4z2 = -33z + 33z + 4z2 + -4z2 Combine like terms: -33z + 33z = 0 27 + 33z + -4z2 = 0 + 4z2 + -4z2 27 + 33z + -4z2 = 4z2 + -4z2 Combine like terms: 4z2 + -4z2 = 0 27 + 33z + -4z2 = 0 Factor a trinomial. (9 + -1z)(3 + 4z) = 0Subproblem 1
Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9Subproblem 2
Set the factor '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 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 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75Solution
z = {9, -0.75}
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