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Simplifying 8g3 + -2g2 = 2g3 + -5g2 Reorder the terms: -2g2 + 8g3 = 2g3 + -5g2 Reorder the terms: -2g2 + 8g3 = -5g2 + 2g3 Solving -2g2 + 8g3 = -5g2 + 2g3 Solving for variable 'g'. Reorder the terms: -2g2 + 5g2 + 8g3 + -2g3 = -5g2 + 2g3 + 5g2 + -2g3 Combine like terms: -2g2 + 5g2 = 3g2 3g2 + 8g3 + -2g3 = -5g2 + 2g3 + 5g2 + -2g3 Combine like terms: 8g3 + -2g3 = 6g3 3g2 + 6g3 = -5g2 + 2g3 + 5g2 + -2g3 Reorder the terms: 3g2 + 6g3 = -5g2 + 5g2 + 2g3 + -2g3 Combine like terms: -5g2 + 5g2 = 0 3g2 + 6g3 = 0 + 2g3 + -2g3 3g2 + 6g3 = 2g3 + -2g3 Combine like terms: 2g3 + -2g3 = 0 3g2 + 6g3 = 0 Factor out the Greatest Common Factor (GCF), '3g2'. 3g2(1 + 2g) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'g2' equal to zero and attempt to solve: Simplifying g2 = 0 Solving g2 = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g2 = 0 Take the square root of each side: g = {0}Subproblem 2
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, -0.5}
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