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Simplifying (g + -9)(2g + 1) = 0 Reorder the terms: (-9 + g)(2g + 1) = 0 Reorder the terms: (-9 + g)(1 + 2g) = 0 Multiply (-9 + g) * (1 + 2g) (-9(1 + 2g) + g(1 + 2g)) = 0 ((1 * -9 + 2g * -9) + g(1 + 2g)) = 0 ((-9 + -18g) + g(1 + 2g)) = 0 (-9 + -18g + (1 * g + 2g * g)) = 0 (-9 + -18g + (1g + 2g2)) = 0 Combine like terms: -18g + 1g = -17g (-9 + -17g + 2g2) = 0 Solving -9 + -17g + 2g2 = 0 Solving for variable 'g'. Factor a trinomial. (-1 + -2g)(9 + -1g) = 0Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(9 + -1g)' equal to zero and attempt to solve: Simplifying 9 + -1g = 0 Solving 9 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1g = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1g = 0 + -9 -1g = 0 + -9 Combine like terms: 0 + -9 = -9 -1g = -9 Divide each side by '-1'. g = 9 Simplifying g = 9Solution
g = {-0.5, 9}
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