ln(2x+1)*ln(9-4x)=0

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Solution for ln(2x+1)*ln(9-4x)=0 equation: 


Simplifying
ln(2x + 1) * ln(9 + -4x) = 0

Reorder the terms:
ln(1 + 2x) * ln(9 + -4x) = 0

Reorder the terms for easier multiplication:
ln * ln(1 + 2x)(9 + -4x) = 0

Multiply ln * ln
l2n2(1 + 2x)(9 + -4x) = 0

Multiply (1 + 2x) * (9 + -4x)
l2n2(1(9 + -4x) + 2x * (9 + -4x)) = 0
l2n2((9 * 1 + -4x * 1) + 2x * (9 + -4x)) = 0
l2n2((9 + -4x) + 2x * (9 + -4x)) = 0
l2n2(9 + -4x + (9 * 2x + -4x * 2x)) = 0
l2n2(9 + -4x + (18x + -8x2)) = 0

Combine like terms: -4x + 18x = 14x
l2n2(9 + 14x + -8x2) = 0
(9 * l2n2 + 14x * l2n2 + -8x2 * l2n2) = 0
(9l2n2 + 14l2n2x + -8l2n2x2) = 0

Solving
9l2n2 + 14l2n2x + -8l2n2x2 = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'l2n2'.
l2n2(9 + 14x + -8x2) = 0

Factor a trinomial.
l2n2((9 + -4x)(1 + 2x)) = 0


Subproblem 1
Set the factor 'l2n2' equal to zero and attempt to solve:

Simplifying
l2n2 = 0

Solving
l2n2 = 0

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

Simplifying
l2n2 = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Add '4x' to each side of the equation.
-4x + 4x = -9 + 4x

Combine like terms: -4x + 4x = 0
0 = -9 + 4x

Simplifying
0 = -9 + 4x

The solution to this equation could not be determined.

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

Subproblem 3
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Add '-2x' to each side of the equation.
2x + -2x = -1 + -2x

Combine like terms: 2x + -2x = 0
0 = -1 + -2x

Simplifying
0 = -1 + -2x

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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