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Simplifying (3g + 5)(g + -2) = 0 Reorder the terms: (5 + 3g)(g + -2) = 0 Reorder the terms: (5 + 3g)(-2 + g) = 0 Multiply (5 + 3g) * (-2 + g) (5(-2 + g) + 3g * (-2 + g)) = 0 ((-2 * 5 + g * 5) + 3g * (-2 + g)) = 0 ((-10 + 5g) + 3g * (-2 + g)) = 0 (-10 + 5g + (-2 * 3g + g * 3g)) = 0 (-10 + 5g + (-6g + 3g2)) = 0 Combine like terms: 5g + -6g = -1g (-10 + -1g + 3g2) = 0 Solving -10 + -1g + 3g2 = 0 Solving for variable 'g'. Factor a trinomial. (-5 + -3g)(2 + -1g) = 0Subproblem 1
Set the factor '(-5 + -3g)' equal to zero and attempt to solve: Simplifying -5 + -3g = 0 Solving -5 + -3g = 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 + -3g = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3g = 0 + 5 -3g = 0 + 5 Combine like terms: 0 + 5 = 5 -3g = 5 Divide each side by '-3'. g = -1.666666667 Simplifying g = -1.666666667Subproblem 2
Set the factor '(2 + -1g)' equal to zero and attempt to solve: Simplifying 2 + -1g = 0 Solving 2 + -1g = 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 + -1g = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1g = 0 + -2 -1g = 0 + -2 Combine like terms: 0 + -2 = -2 -1g = -2 Divide each side by '-1'. g = 2 Simplifying g = 2Solution
g = {-1.666666667, 2}
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