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Simplifying 9000 = l(l + -45) Reorder the terms: 9000 = l(-45 + l) 9000 = (-45 * l + l * l) 9000 = (-45l + l2) Solving 9000 = -45l + l2 Solving for variable 'l'. Reorder the terms: 9000 + 45l + -1l2 = -45l + 45l + l2 + -1l2 Combine like terms: -45l + 45l = 0 9000 + 45l + -1l2 = 0 + l2 + -1l2 9000 + 45l + -1l2 = l2 + -1l2 Combine like terms: l2 + -1l2 = 0 9000 + 45l + -1l2 = 0 Factor a trinomial. (120 + -1l)(75 + l) = 0Subproblem 1
Set the factor '(120 + -1l)' equal to zero and attempt to solve: Simplifying 120 + -1l = 0 Solving 120 + -1l = 0 Move all terms containing l to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + -120 + -1l = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -1l = 0 + -120 -1l = 0 + -120 Combine like terms: 0 + -120 = -120 -1l = -120 Divide each side by '-1'. l = 120 Simplifying l = 120Subproblem 2
Set the factor '(75 + l)' equal to zero and attempt to solve: Simplifying 75 + l = 0 Solving 75 + l = 0 Move all terms containing l to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + l = 0 + -75 Combine like terms: 75 + -75 = 0 0 + l = 0 + -75 l = 0 + -75 Combine like terms: 0 + -75 = -75 l = -75 Simplifying l = -75Solution
l = {120, -75}
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