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Simplifying (4g + 5)(2g + 10) = 0 Reorder the terms: (5 + 4g)(2g + 10) = 0 Reorder the terms: (5 + 4g)(10 + 2g) = 0 Multiply (5 + 4g) * (10 + 2g) (5(10 + 2g) + 4g * (10 + 2g)) = 0 ((10 * 5 + 2g * 5) + 4g * (10 + 2g)) = 0 ((50 + 10g) + 4g * (10 + 2g)) = 0 (50 + 10g + (10 * 4g + 2g * 4g)) = 0 (50 + 10g + (40g + 8g2)) = 0 Combine like terms: 10g + 40g = 50g (50 + 50g + 8g2) = 0 Solving 50 + 50g + 8g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 25g + 4g2) = 0 Factor a trinomial. 2((5 + g)(5 + 4g)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + g)' equal to zero and attempt to solve: Simplifying 5 + g = 0 Solving 5 + g = 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 + g = 0 + -5 Combine like terms: 5 + -5 = 0 0 + g = 0 + -5 g = 0 + -5 Combine like terms: 0 + -5 = -5 g = -5 Simplifying g = -5Subproblem 2
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 = -1.25Solution
g = {-5, -1.25}
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