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Simplifying 27z2 + 3z + -2 = 0 Reorder the terms: -2 + 3z + 27z2 = 0 Solving -2 + 3z + 27z2 = 0 Solving for variable 'z'. Factor a trinomial. (-1 + -3z)(2 + -9z) = 0Subproblem 1
Set the factor '(-1 + -3z)' equal to zero and attempt to solve: Simplifying -1 + -3z = 0 Solving -1 + -3z = 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 + -3z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3z = 0 + 1 -3z = 0 + 1 Combine like terms: 0 + 1 = 1 -3z = 1 Divide each side by '-3'. z = -0.3333333333 Simplifying z = -0.3333333333Subproblem 2
Set the factor '(2 + -9z)' equal to zero and attempt to solve: Simplifying 2 + -9z = 0 Solving 2 + -9z = 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 + -9z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9z = 0 + -2 -9z = 0 + -2 Combine like terms: 0 + -2 = -2 -9z = -2 Divide each side by '-9'. z = 0.2222222222 Simplifying z = 0.2222222222Solution
z = {-0.3333333333, 0.2222222222}
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