200L+6Lm=500L-6Lm

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Solution for 200L+6Lm=500L-6Lm equation: 


Simplifying
200L + 6Lm = 500L + -6Lm

Solving
200L + 6mL = 500L + -6mL

Solving for variable 'L'.

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

Add '-500L' to each side of the equation.
200L + -500L + 6mL = 500L + -500L + -6mL

Combine like terms: 200L + -500L = -300L
-300L + 6mL = 500L + -500L + -6mL

Combine like terms: 500L + -500L = 0
-300L + 6mL = 0 + -6mL
-300L + 6mL = -6mL

Add '6mL' to each side of the equation.
-300L + 6mL + 6mL = -6mL + 6mL

Combine like terms: 6mL + 6mL = 12mL
-300L + 12mL = -6mL + 6mL

Combine like terms: -6mL + 6mL = 0
-300L + 12mL = 0

Factor out the Greatest Common Factor (GCF), '12L'.
12L(-25 + m) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'L' equal to zero and attempt to solve:

Simplifying
L = 0

Solving
L = 0

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

Simplifying
L = 0

Subproblem 2
Set the factor '(-25 + m)' equal to zero and attempt to solve:

Simplifying
-25 + m = 0

Solving
-25 + m = 0

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

Add '25' to each side of the equation.
-25 + 25 + m = 0 + 25

Combine like terms: -25 + 25 = 0
0 + m = 0 + 25
m = 0 + 25

Combine like terms: 0 + 25 = 25
m = 25

Add '-1m' to each side of the equation.
m + -1m = 25 + -1m

Combine like terms: m + -1m = 0
0 = 25 + -1m

Simplifying
0 = 25 + -1m

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
L = {0}

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