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Simplifying 4g(3g + -2) + -2g(5 + 4g) = 0 Reorder the terms: 4g(-2 + 3g) + -2g(5 + 4g) = 0 (-2 * 4g + 3g * 4g) + -2g(5 + 4g) = 0 (-8g + 12g2) + -2g(5 + 4g) = 0 -8g + 12g2 + (5 * -2g + 4g * -2g) = 0 -8g + 12g2 + (-10g + -8g2) = 0 Reorder the terms: -8g + -10g + 12g2 + -8g2 = 0 Combine like terms: -8g + -10g = -18g -18g + 12g2 + -8g2 = 0 Combine like terms: 12g2 + -8g2 = 4g2 -18g + 4g2 = 0 Solving -18g + 4g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '2g'. 2g(-9 + 2g) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'g' equal to zero and attempt to solve: Simplifying g = 0 Solving g = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g = 0Subproblem 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 = {0, 4.5}
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