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Simplifying L(L + 4) = 96 Reorder the terms: L(4 + L) = 96 (4 * L + L * L) = 96 (4L + L2) = 96 Solving 4L + L2 = 96 Solving for variable 'L'. Reorder the terms: -96 + 4L + L2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 4L + L2 = 0 Factor a trinomial. (-12 + -1L)(8 + -1L) = 0Subproblem 1
Set the factor '(-12 + -1L)' equal to zero and attempt to solve: Simplifying -12 + -1L = 0 Solving -12 + -1L = 0 Move all terms containing L to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1L = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1L = 0 + 12 -1L = 0 + 12 Combine like terms: 0 + 12 = 12 -1L = 12 Divide each side by '-1'. L = -12 Simplifying L = -12Subproblem 2
Set the factor '(8 + -1L)' equal to zero and attempt to solve: Simplifying 8 + -1L = 0 Solving 8 + -1L = 0 Move all terms containing L to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1L = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1L = 0 + -8 -1L = 0 + -8 Combine like terms: 0 + -8 = -8 -1L = -8 Divide each side by '-1'. L = 8 Simplifying L = 8Solution
L = {-12, 8}
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