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Simplifying 12Z2 + -76Z + -56 = 0 Reorder the terms: -56 + -76Z + 12Z2 = 0 Solving -56 + -76Z + 12Z2 = 0 Solving for variable 'Z'. Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + -19Z + 3Z2) = 0 Factor a trinomial. 4((-2 + -3Z)(7 + -1Z)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -3Z)' equal to zero and attempt to solve: Simplifying -2 + -3Z = 0 Solving -2 + -3Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3Z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3Z = 0 + 2 -3Z = 0 + 2 Combine like terms: 0 + 2 = 2 -3Z = 2 Divide each side by '-3'. Z = -0.6666666667 Simplifying Z = -0.6666666667Subproblem 2
Set the factor '(7 + -1Z)' equal to zero and attempt to solve: Simplifying 7 + -1Z = 0 Solving 7 + -1Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1Z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1Z = 0 + -7 -1Z = 0 + -7 Combine like terms: 0 + -7 = -7 -1Z = -7 Divide each side by '-1'. Z = 7 Simplifying Z = 7Solution
Z = {-0.6666666667, 7}
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