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Simplifying (2g + -2)(4g + -9) = 133 Reorder the terms: (-2 + 2g)(4g + -9) = 133 Reorder the terms: (-2 + 2g)(-9 + 4g) = 133 Multiply (-2 + 2g) * (-9 + 4g) (-2(-9 + 4g) + 2g * (-9 + 4g)) = 133 ((-9 * -2 + 4g * -2) + 2g * (-9 + 4g)) = 133 ((18 + -8g) + 2g * (-9 + 4g)) = 133 (18 + -8g + (-9 * 2g + 4g * 2g)) = 133 (18 + -8g + (-18g + 8g2)) = 133 Combine like terms: -8g + -18g = -26g (18 + -26g + 8g2) = 133 Solving 18 + -26g + 8g2 = 133 Solving for variable 'g'. Reorder the terms: 18 + -133 + -26g + 8g2 = 133 + -133 Combine like terms: 18 + -133 = -115 -115 + -26g + 8g2 = 133 + -133 Combine like terms: 133 + -133 = 0 -115 + -26g + 8g2 = 0 Factor a trinomial. (-5 + -2g)(23 + -4g) = 0Subproblem 1
Set the factor '(-5 + -2g)' equal to zero and attempt to solve: Simplifying -5 + -2g = 0 Solving -5 + -2g = 0 Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2g = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2g = 0 + 5 -2g = 0 + 5 Combine like terms: 0 + 5 = 5 -2g = 5 Divide each side by '-2'. g = -2.5 Simplifying g = -2.5Subproblem 2
Set the factor '(23 + -4g)' equal to zero and attempt to solve: Simplifying 23 + -4g = 0 Solving 23 + -4g = 0 Move all terms containing g to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -4g = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -4g = 0 + -23 -4g = 0 + -23 Combine like terms: 0 + -23 = -23 -4g = -23 Divide each side by '-4'. g = 5.75 Simplifying g = 5.75Solution
g = {-2.5, 5.75}
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