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Simplifying (L)(L + 2) * 4 = 192 Reorder the terms: L(2 + L) * 4 = 192 Reorder the terms for easier multiplication: 4L(2 + L) = 192 (2 * 4L + L * 4L) = 192 (8L + 4L2) = 192 Solving 8L + 4L2 = 192 Solving for variable 'L'. Reorder the terms: -192 + 8L + 4L2 = 192 + -192 Combine like terms: 192 + -192 = 0 -192 + 8L + 4L2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-48 + 2L + L2) = 0 Factor a trinomial. 4((-8 + -1L)(6 + -1L)) = 0 Ignore the factor 4.Subproblem 1
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 = -8Subproblem 2
Set the factor '(6 + -1L)' equal to zero and attempt to solve: Simplifying 6 + -1L = 0 Solving 6 + -1L = 0 Move all terms containing L to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1L = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1L = 0 + -6 -1L = 0 + -6 Combine like terms: 0 + -6 = -6 -1L = -6 Divide each side by '-1'. L = 6 Simplifying L = 6Solution
L = {-8, 6}
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