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Simplifying 6z2 + 17z + 12 = 0 Reorder the terms: 12 + 17z + 6z2 = 0 Solving 12 + 17z + 6z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + 2z)(4 + 3z) = 0Subproblem 1
Set the factor '(3 + 2z)' equal to zero and attempt to solve: Simplifying 3 + 2z = 0 Solving 3 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2z = 0 + -3 2z = 0 + -3 Combine like terms: 0 + -3 = -3 2z = -3 Divide each side by '2'. z = -1.5 Simplifying z = -1.5Subproblem 2
Set the factor '(4 + 3z)' equal to zero and attempt to solve: Simplifying 4 + 3z = 0 Solving 4 + 3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3z = 0 + -4 3z = 0 + -4 Combine like terms: 0 + -4 = -4 3z = -4 Divide each side by '3'. z = -1.333333333 Simplifying z = -1.333333333Solution
z = {-1.5, -1.333333333}
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