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Simplifying (4g + -7)(2g + -1) = 0 Reorder the terms: (-7 + 4g)(2g + -1) = 0 Reorder the terms: (-7 + 4g)(-1 + 2g) = 0 Multiply (-7 + 4g) * (-1 + 2g) (-7(-1 + 2g) + 4g * (-1 + 2g)) = 0 ((-1 * -7 + 2g * -7) + 4g * (-1 + 2g)) = 0 ((7 + -14g) + 4g * (-1 + 2g)) = 0 (7 + -14g + (-1 * 4g + 2g * 4g)) = 0 (7 + -14g + (-4g + 8g2)) = 0 Combine like terms: -14g + -4g = -18g (7 + -18g + 8g2) = 0 Solving 7 + -18g + 8g2 = 0 Solving for variable 'g'. Factor a trinomial. (1 + -2g)(7 + -4g) = 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 '(7 + -4g)' equal to zero and attempt to solve: Simplifying 7 + -4g = 0 Solving 7 + -4g = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4g = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4g = 0 + -7 -4g = 0 + -7 Combine like terms: 0 + -7 = -7 -4g = -7 Divide each side by '-4'. g = 1.75 Simplifying g = 1.75Solution
g = {0.5, 1.75}
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