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Simplifying G(3b) = 3b2 + -3b Remove parenthesis around (3b) G * 3b = 3b2 + -3b Reorder the terms for easier multiplication: 3G * b = 3b2 + -3b Multiply G * b 3bG = 3b2 + -3b Reorder the terms: 3bG = -3b + 3b2 Solving 3bG = -3b + 3b2 Solving for variable 'b'. Reorder the terms: 3b + 3bG + -3b2 = -3b + 3b2 + 3b + -3b2 Reorder the terms: 3b + 3bG + -3b2 = -3b + 3b + 3b2 + -3b2 Combine like terms: -3b + 3b = 0 3b + 3bG + -3b2 = 0 + 3b2 + -3b2 3b + 3bG + -3b2 = 3b2 + -3b2 Combine like terms: 3b2 + -3b2 = 0 3b + 3bG + -3b2 = 0 Factor out the Greatest Common Factor (GCF), '3b'. 3b(1 + G + -1b) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(1 + G + -1b)' equal to zero and attempt to solve: Simplifying 1 + G + -1b = 0 Solving 1 + G + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + G + -1 + -1b = 0 + -1 Reorder the terms: 1 + -1 + G + -1b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + G + -1b = 0 + -1 G + -1b = 0 + -1 Combine like terms: 0 + -1 = -1 G + -1b = -1 Add '-1G' to each side of the equation. G + -1G + -1b = -1 + -1G Combine like terms: G + -1G = 0 0 + -1b = -1 + -1G -1b = -1 + -1G Divide each side by '-1'. b = 1 + G Simplifying b = 1 + GSolution
b = {0, 1 + G}
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