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Simplifying 12z2 + 5z + -2 = 0 Reorder the terms: -2 + 5z + 12z2 = 0 Solving -2 + 5z + 12z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + -3z)(1 + -4z) = 0Subproblem 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 '(1 + -4z)' equal to zero and attempt to solve: Simplifying 1 + -4z = 0 Solving 1 + -4z = 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 + -4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4z = 0 + -1 -4z = 0 + -1 Combine like terms: 0 + -1 = -1 -4z = -1 Divide each side by '-4'. z = 0.25 Simplifying z = 0.25Solution
z = {-0.6666666667, 0.25}
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