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Simplifying (g + 10)(2g + -5) = 0 Reorder the terms: (10 + g)(2g + -5) = 0 Reorder the terms: (10 + g)(-5 + 2g) = 0 Multiply (10 + g) * (-5 + 2g) (10(-5 + 2g) + g(-5 + 2g)) = 0 ((-5 * 10 + 2g * 10) + g(-5 + 2g)) = 0 ((-50 + 20g) + g(-5 + 2g)) = 0 (-50 + 20g + (-5 * g + 2g * g)) = 0 (-50 + 20g + (-5g + 2g2)) = 0 Combine like terms: 20g + -5g = 15g (-50 + 15g + 2g2) = 0 Solving -50 + 15g + 2g2 = 0 Solving for variable 'g'. Factor a trinomial. (-10 + -1g)(5 + -2g) = 0Subproblem 1
Set the factor '(-10 + -1g)' equal to zero and attempt to solve: Simplifying -10 + -1g = 0 Solving -10 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1g = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1g = 0 + 10 -1g = 0 + 10 Combine like terms: 0 + 10 = 10 -1g = 10 Divide each side by '-1'. g = -10 Simplifying g = -10Subproblem 2
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 = 2.5Solution
g = {-10, 2.5}
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