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Simplifying 12z2 + 74z + 44 = 0 Reorder the terms: 44 + 74z + 12z2 = 0 Solving 44 + 74z + 12z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(22 + 37z + 6z2) = 0 Factor a trinomial. 2((11 + 2z)(2 + 3z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 2z)' equal to zero and attempt to solve: Simplifying 11 + 2z = 0 Solving 11 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 2z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 2z = 0 + -11 2z = 0 + -11 Combine like terms: 0 + -11 = -11 2z = -11 Divide each side by '2'. z = -5.5 Simplifying z = -5.5Subproblem 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 = {-5.5, -0.6666666667}
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