15ln^2(2x+4)=6x+12

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Solution for 15ln^2(2x+4)=6x+12 equation: 


Simplifying
15ln2(2x + 4) = 6x + 12

Reorder the terms:
15ln2(4 + 2x) = 6x + 12
(4 * 15ln2 + 2x * 15ln2) = 6x + 12
(60ln2 + 30ln2x) = 6x + 12

Reorder the terms:
60ln2 + 30ln2x = 12 + 6x

Solving
60ln2 + 30ln2x = 12 + 6x

Solving for variable 'l'.

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

Reorder the terms:
-12 + 60ln2 + 30ln2x + -6x = 12 + 6x + -12 + -6x

Reorder the terms:
-12 + 60ln2 + 30ln2x + -6x = 12 + -12 + 6x + -6x

Combine like terms: 12 + -12 = 0
-12 + 60ln2 + 30ln2x + -6x = 0 + 6x + -6x
-12 + 60ln2 + 30ln2x + -6x = 6x + -6x

Combine like terms: 6x + -6x = 0
-12 + 60ln2 + 30ln2x + -6x = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 10ln2 + 5ln2x + -1x) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-2 + 10ln2 + 5ln2x + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + 10ln2 + 5ln2x + -1x = 0

Solving
-2 + 10ln2 + 5ln2x + -1x = 0

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

Add '2' to each side of the equation.
-2 + 10ln2 + 5ln2x + 2 + -1x = 0 + 2

Reorder the terms:
-2 + 2 + 10ln2 + 5ln2x + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 10ln2 + 5ln2x + -1x = 0 + 2
10ln2 + 5ln2x + -1x = 0 + 2

Combine like terms: 0 + 2 = 2
10ln2 + 5ln2x + -1x = 2

Add 'x' to each side of the equation.
10ln2 + 5ln2x + -1x + x = 2 + x

Combine like terms: -1x + x = 0
10ln2 + 5ln2x + 0 = 2 + x
10ln2 + 5ln2x = 2 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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