0=L^2-17L+60

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Solution for 0=L^2-17L+60 equation:


Simplifying
0 = L2 + -17L + 60

Reorder the terms:
0 = 60 + -17L + L2

Solving
0 = 60 + -17L + L2

Solving for variable 'L'.

Combine like terms: 0 + -60 = -60
-60 + 17L + -1L2 = 60 + -17L + L2 + -60 + 17L + -1L2

Reorder the terms:
-60 + 17L + -1L2 = 60 + -60 + -17L + 17L + L2 + -1L2

Combine like terms: 60 + -60 = 0
-60 + 17L + -1L2 = 0 + -17L + 17L + L2 + -1L2
-60 + 17L + -1L2 = -17L + 17L + L2 + -1L2

Combine like terms: -17L + 17L = 0
-60 + 17L + -1L2 = 0 + L2 + -1L2
-60 + 17L + -1L2 = L2 + -1L2

Combine like terms: L2 + -1L2 = 0
-60 + 17L + -1L2 = 0

Factor a trinomial.
(-12 + L)(5 + -1L) = 0

Subproblem 1

Set the factor '(-12 + L)' equal to zero and attempt to solve: Simplifying -12 + L = 0 Solving -12 + L = 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 + L = 0 + 12 Combine like terms: -12 + 12 = 0 0 + L = 0 + 12 L = 0 + 12 Combine like terms: 0 + 12 = 12 L = 12 Simplifying L = 12

Subproblem 2

Set the factor '(5 + -1L)' equal to zero and attempt to solve: Simplifying 5 + -1L = 0 Solving 5 + -1L = 0 Move all terms containing L to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1L = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1L = 0 + -5 -1L = 0 + -5 Combine like terms: 0 + -5 = -5 -1L = -5 Divide each side by '-1'. L = 5 Simplifying L = 5

Solution

L = {12, 5}

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