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Simplifying 34g3 + 51g2 + 17g = 0 Reorder the terms: 17g + 51g2 + 34g3 = 0 Solving 17g + 51g2 + 34g3 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '17g'. 17g(1 + 3g + 2g2) = 0 Factor a trinomial. 17g((1 + g)(1 + 2g)) = 0 Ignore the factor 17.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 '(1 + g)' equal to zero and attempt to solve: Simplifying 1 + g = 0 Solving 1 + g = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + g = 0 + -1 Combine like terms: 1 + -1 = 0 0 + g = 0 + -1 g = 0 + -1 Combine like terms: 0 + -1 = -1 g = -1 Simplifying g = -1Subproblem 3
Set the factor '(1 + 2g)' equal to zero and attempt to solve: Simplifying 1 + 2g = 0 Solving 1 + 2g = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2g = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2g = 0 + -1 2g = 0 + -1 Combine like terms: 0 + -1 = -1 2g = -1 Divide each side by '2'. g = -0.5 Simplifying g = -0.5Solution
g = {0, -1, -0.5}
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