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Simplifying (g + -3)(2g + -9) = 0 Reorder the terms: (-3 + g)(2g + -9) = 0 Reorder the terms: (-3 + g)(-9 + 2g) = 0 Multiply (-3 + g) * (-9 + 2g) (-3(-9 + 2g) + g(-9 + 2g)) = 0 ((-9 * -3 + 2g * -3) + g(-9 + 2g)) = 0 ((27 + -6g) + g(-9 + 2g)) = 0 (27 + -6g + (-9 * g + 2g * g)) = 0 (27 + -6g + (-9g + 2g2)) = 0 Combine like terms: -6g + -9g = -15g (27 + -15g + 2g2) = 0 Solving 27 + -15g + 2g2 = 0 Solving for variable 'g'. Factor a trinomial. (3 + -1g)(9 + -2g) = 0Subproblem 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 '(9 + -2g)' equal to zero and attempt to solve: Simplifying 9 + -2g = 0 Solving 9 + -2g = 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 + -2g = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2g = 0 + -9 -2g = 0 + -9 Combine like terms: 0 + -9 = -9 -2g = -9 Divide each side by '-2'. g = 4.5 Simplifying g = 4.5Solution
g = {3, 4.5}
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