80=(2L-60)L

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Solution for 80=(2L-60)L equation: 


Simplifying
80 = (2L + -60) * L

Reorder the terms:
80 = (-60 + 2L) * L

Reorder the terms for easier multiplication:
80 = L(-60 + 2L)
80 = (-60 * L + 2L * L)
80 = (-60L + 2L2)

Solving
80 = -60L + 2L2

Solving for variable 'L'.

Reorder the terms:
80 + 60L + -2L2 = -60L + 60L + 2L2 + -2L2

Combine like terms: -60L + 60L = 0
80 + 60L + -2L2 = 0 + 2L2 + -2L2
80 + 60L + -2L2 = 2L2 + -2L2

Combine like terms: 2L2 + -2L2 = 0
80 + 60L + -2L2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + 30L + -1L2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(40 + 30L + -1L2)' equal to zero and attempt to solve:

Simplifying
40 + 30L + -1L2 = 0

Solving
40 + 30L + -1L2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-40 + -30L + L2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -30L + 40 + L2 = 0 + 40

Reorder the terms:
-40 + 40 + -30L + L2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -30L + L2 = 0 + 40
-30L + L2 = 0 + 40

Combine like terms: 0 + 40 = 40
-30L + L2 = 40

The L term is -30L.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30L + 225 + L2 = 40 + 225

Reorder the terms:
225 + -30L + L2 = 40 + 225

Combine like terms: 40 + 225 = 265
225 + -30L + L2 = 265

Factor a perfect square on the left side:
(L + -15)(L + -15) = 265

Calculate the square root of the right side: 16.278820596

Break this problem into two subproblems by setting 
(L + -15) equal to 16.278820596 and -16.278820596.


Subproblem 1
L + -15 = 16.278820596

Simplifying
L + -15 = 16.278820596

Reorder the terms:
-15 + L = 16.278820596

Solving
-15 + L = 16.278820596

Solving for variable 'L'.

Move all terms containing L to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + L = 16.278820596 + 15

Combine like terms: -15 + 15 = 0
0 + L = 16.278820596 + 15
L = 16.278820596 + 15

Combine like terms: 16.278820596 + 15 = 31.278820596
L = 31.278820596

Simplifying
L = 31.278820596


Subproblem 2
L + -15 = -16.278820596

Simplifying
L + -15 = -16.278820596

Reorder the terms:
-15 + L = -16.278820596

Solving
-15 + L = -16.278820596

Solving for variable 'L'.

Move all terms containing L to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + L = -16.278820596 + 15

Combine like terms: -15 + 15 = 0
0 + L = -16.278820596 + 15
L = -16.278820596 + 15

Combine like terms: -16.278820596 + 15 = -1.278820596
L = -1.278820596

Simplifying
L = -1.278820596


Solution
The solution to the problem is based on the solutions
from the subproblems.
L = {31.278820596, -1.278820596}
Solution
L = {31.278820596, -1.278820596}

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