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Simplifying 2z2 + -22z + -24 = 0 Reorder the terms: -24 + -22z + 2z2 = 0 Solving -24 + -22z + 2z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -11z + z2) = 0 Factor a trinomial. 2((-1 + -1z)(12 + -1z)) = 0 Ignore the factor 2.Subproblem 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 '(12 + -1z)' equal to zero and attempt to solve: Simplifying 12 + -1z = 0 Solving 12 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1z = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1z = 0 + -12 -1z = 0 + -12 Combine like terms: 0 + -12 = -12 -1z = -12 Divide each side by '-1'. z = 12 Simplifying z = 12Solution
z = {-1, 12}
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