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Simplifying 6g3 + -2g2 + 4g = 0 Reorder the terms: 4g + -2g2 + 6g3 = 0 Solving 4g + -2g2 + 6g3 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '2g'. 2g(2 + -1g + 3g2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'g' equal to zero and attempt to solve: Simplifying g = 0 Solving g = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g = 0Subproblem 2
Set the factor '(2 + -1g + 3g2)' equal to zero and attempt to solve: Simplifying 2 + -1g + 3g2 = 0 Solving 2 + -1g + 3g2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -0.3333333333g + g2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.3333333333g + -0.6666666667 + g2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.3333333333g + g2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.3333333333g + g2 = 0 + -0.6666666667 -0.3333333333g + g2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.3333333333g + g2 = -0.6666666667 The g term is -0.3333333333g. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333g + 0.02777777779 + g2 = -0.6666666667 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333g + g2 = -0.6666666667 + 0.02777777779 Combine like terms: -0.6666666667 + 0.02777777779 = -0.63888888891 0.02777777779 + -0.3333333333g + g2 = -0.63888888891 Factor a perfect square on the left side: (g + -0.1666666667)(g + -0.1666666667) = -0.63888888891 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
g = {0}
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