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Simplifying 18z2 + 33z + 14 = 0 Reorder the terms: 14 + 33z + 18z2 = 0 Solving 14 + 33z + 18z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + 6z)(2 + 3z) = 0Subproblem 1
Set the factor '(7 + 6z)' equal to zero and attempt to solve: Simplifying 7 + 6z = 0 Solving 7 + 6z = 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 + 6z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6z = 0 + -7 6z = 0 + -7 Combine like terms: 0 + -7 = -7 6z = -7 Divide each side by '6'. z = -1.166666667 Simplifying z = -1.166666667Subproblem 2
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 = -0.6666666667Solution
z = {-1.166666667, -0.6666666667}
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