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Simplifying g2 + -105 = -4g2 + 20g Reorder the terms: -105 + g2 = -4g2 + 20g Reorder the terms: -105 + g2 = 20g + -4g2 Solving -105 + g2 = 20g + -4g2 Solving for variable 'g'. Reorder the terms: -105 + -20g + g2 + 4g2 = 20g + -4g2 + -20g + 4g2 Combine like terms: g2 + 4g2 = 5g2 -105 + -20g + 5g2 = 20g + -4g2 + -20g + 4g2 Reorder the terms: -105 + -20g + 5g2 = 20g + -20g + -4g2 + 4g2 Combine like terms: 20g + -20g = 0 -105 + -20g + 5g2 = 0 + -4g2 + 4g2 -105 + -20g + 5g2 = -4g2 + 4g2 Combine like terms: -4g2 + 4g2 = 0 -105 + -20g + 5g2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-21 + -4g + g2) = 0 Factor a trinomial. 5((-3 + -1g)(7 + -1g)) = 0 Ignore the factor 5.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 '(7 + -1g)' equal to zero and attempt to solve: Simplifying 7 + -1g = 0 Solving 7 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1g = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1g = 0 + -7 -1g = 0 + -7 Combine like terms: 0 + -7 = -7 -1g = -7 Divide each side by '-1'. g = 7 Simplifying g = 7Solution
g = {-3, 7}
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