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Simplifying (g + 17)(g + -2) = 20 Reorder the terms: (17 + g)(g + -2) = 20 Reorder the terms: (17 + g)(-2 + g) = 20 Multiply (17 + g) * (-2 + g) (17(-2 + g) + g(-2 + g)) = 20 ((-2 * 17 + g * 17) + g(-2 + g)) = 20 ((-34 + 17g) + g(-2 + g)) = 20 (-34 + 17g + (-2 * g + g * g)) = 20 (-34 + 17g + (-2g + g2)) = 20 Combine like terms: 17g + -2g = 15g (-34 + 15g + g2) = 20 Solving -34 + 15g + g2 = 20 Solving for variable 'g'. Reorder the terms: -34 + -20 + 15g + g2 = 20 + -20 Combine like terms: -34 + -20 = -54 -54 + 15g + g2 = 20 + -20 Combine like terms: 20 + -20 = 0 -54 + 15g + g2 = 0 Factor a trinomial. (-18 + -1g)(3 + -1g) = 0Subproblem 1
Set the factor '(-18 + -1g)' equal to zero and attempt to solve: Simplifying -18 + -1g = 0 Solving -18 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + -1g = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1g = 0 + 18 -1g = 0 + 18 Combine like terms: 0 + 18 = 18 -1g = 18 Divide each side by '-1'. g = -18 Simplifying g = -18Subproblem 2
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 = 3Solution
g = {-18, 3}
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