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Simplifying 3z * 3z + -3z + -6 = 0 Reorder the terms for easier multiplication: 3 * 3z * z + -3z + -6 = 0 Multiply 3 * 3 9z * z + -3z + -6 = 0 Multiply z * z 9z2 + -3z + -6 = 0 Reorder the terms: -6 + -3z + 9z2 = 0 Solving -6 + -3z + 9z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + -1z + 3z2) = 0 Factor a trinomial. 3((-2 + -3z)(1 + -1z)) = 0 Ignore the factor 3.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 '(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 = 1Solution
z = {-0.6666666667, 1}
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