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Simplifying (3g + -5)(4g + -3) = 0 Reorder the terms: (-5 + 3g)(4g + -3) = 0 Reorder the terms: (-5 + 3g)(-3 + 4g) = 0 Multiply (-5 + 3g) * (-3 + 4g) (-5(-3 + 4g) + 3g * (-3 + 4g)) = 0 ((-3 * -5 + 4g * -5) + 3g * (-3 + 4g)) = 0 ((15 + -20g) + 3g * (-3 + 4g)) = 0 (15 + -20g + (-3 * 3g + 4g * 3g)) = 0 (15 + -20g + (-9g + 12g2)) = 0 Combine like terms: -20g + -9g = -29g (15 + -29g + 12g2) = 0 Solving 15 + -29g + 12g2 = 0 Solving for variable 'g'. Factor a trinomial. (3 + -4g)(5 + -3g) = 0Subproblem 1
Set the factor '(3 + -4g)' equal to zero and attempt to solve: Simplifying 3 + -4g = 0 Solving 3 + -4g = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4g = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4g = 0 + -3 -4g = 0 + -3 Combine like terms: 0 + -3 = -3 -4g = -3 Divide each side by '-4'. g = 0.75 Simplifying g = 0.75Subproblem 2
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 = 1.666666667Solution
g = {0.75, 1.666666667}
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