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Simplifying (4g + 5)(7g + -2) = 0 Reorder the terms: (5 + 4g)(7g + -2) = 0 Reorder the terms: (5 + 4g)(-2 + 7g) = 0 Multiply (5 + 4g) * (-2 + 7g) (5(-2 + 7g) + 4g * (-2 + 7g)) = 0 ((-2 * 5 + 7g * 5) + 4g * (-2 + 7g)) = 0 ((-10 + 35g) + 4g * (-2 + 7g)) = 0 (-10 + 35g + (-2 * 4g + 7g * 4g)) = 0 (-10 + 35g + (-8g + 28g2)) = 0 Combine like terms: 35g + -8g = 27g (-10 + 27g + 28g2) = 0 Solving -10 + 27g + 28g2 = 0 Solving for variable 'g'. Factor a trinomial. (-5 + -4g)(2 + -7g) = 0Subproblem 1
Set the factor '(-5 + -4g)' equal to zero and attempt to solve: Simplifying -5 + -4g = 0 Solving -5 + -4g = 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 + -4g = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4g = 0 + 5 -4g = 0 + 5 Combine like terms: 0 + 5 = 5 -4g = 5 Divide each side by '-4'. g = -1.25 Simplifying g = -1.25Subproblem 2
Set the factor '(2 + -7g)' equal to zero and attempt to solve: Simplifying 2 + -7g = 0 Solving 2 + -7g = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7g = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7g = 0 + -2 -7g = 0 + -2 Combine like terms: 0 + -2 = -2 -7g = -2 Divide each side by '-7'. g = 0.2857142857 Simplifying g = 0.2857142857Solution
g = {-1.25, 0.2857142857}
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