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Simplifying 30g2 + 50g + -120 = 0 Reorder the terms: -120 + 50g + 30g2 = 0 Solving -120 + 50g + 30g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '10'. 10(-12 + 5g + 3g2) = 0 Factor a trinomial. 10((-3 + -1g)(4 + -3g)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-3 + -1g)' equal to zero and attempt to solve: Simplifying -3 + -1g = 0 Solving -3 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1g = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1g = 0 + 3 -1g = 0 + 3 Combine like terms: 0 + 3 = 3 -1g = 3 Divide each side by '-1'. g = -3 Simplifying g = -3Subproblem 2
Set the factor '(4 + -3g)' equal to zero and attempt to solve: Simplifying 4 + -3g = 0 Solving 4 + -3g = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3g = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3g = 0 + -4 -3g = 0 + -4 Combine like terms: 0 + -4 = -4 -3g = -4 Divide each side by '-3'. g = 1.333333333 Simplifying g = 1.333333333Solution
g = {-3, 1.333333333}
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