Ln(3x^2+5x)=ln(6x+10)

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Solution for Ln(3x^2+5x)=ln(6x+10) equation: 


Simplifying
Ln(3x2 + 5x) = ln(6x + 10)

Reorder the terms:
nL(5x + 3x2) = ln(6x + 10)
(5x * nL + 3x2 * nL) = ln(6x + 10)
(5nxL + 3nx2L) = ln(6x + 10)

Reorder the terms:
5nxL + 3nx2L = ln(10 + 6x)
5nxL + 3nx2L = (10 * ln + 6x * ln)
5nxL + 3nx2L = (10ln + 6lnx)

Solving
5nxL + 3nx2L = 10ln + 6lnx

Solving for variable 'n'.

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

Add '-10ln' to each side of the equation.
5nxL + -10ln + 3nx2L = 10ln + -10ln + 6lnx

Reorder the terms:
-10ln + 5nxL + 3nx2L = 10ln + -10ln + 6lnx

Combine like terms: 10ln + -10ln = 0
-10ln + 5nxL + 3nx2L = 0 + 6lnx
-10ln + 5nxL + 3nx2L = 6lnx

Add '-6lnx' to each side of the equation.
-10ln + 5nxL + -6lnx + 3nx2L = 6lnx + -6lnx

Reorder the terms:
-10ln + -6lnx + 5nxL + 3nx2L = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-10ln + -6lnx + 5nxL + 3nx2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-10l + -6lx + 5xL + 3x2L) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-10l + -6lx + 5xL + 3x2L)' equal to zero and attempt to solve:

Simplifying
-10l + -6lx + 5xL + 3x2L = 0

Solving
-10l + -6lx + 5xL + 3x2L = 0

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

Add '10l' to each side of the equation.
-10l + -6lx + 5xL + 10l + 3x2L = 0 + 10l

Reorder the terms:
-10l + 10l + -6lx + 5xL + 3x2L = 0 + 10l

Combine like terms: -10l + 10l = 0
0 + -6lx + 5xL + 3x2L = 0 + 10l
-6lx + 5xL + 3x2L = 0 + 10l
Remove the zero:
-6lx + 5xL + 3x2L = 10l

Add '6lx' to each side of the equation.
-6lx + 5xL + 6lx + 3x2L = 10l + 6lx

Reorder the terms:
-6lx + 6lx + 5xL + 3x2L = 10l + 6lx

Combine like terms: -6lx + 6lx = 0
0 + 5xL + 3x2L = 10l + 6lx
5xL + 3x2L = 10l + 6lx

Add '-5xL' to each side of the equation.
5xL + -5xL + 3x2L = 10l + 6lx + -5xL

Combine like terms: 5xL + -5xL = 0
0 + 3x2L = 10l + 6lx + -5xL
3x2L = 10l + 6lx + -5xL

Add '-3x2L' to each side of the equation.
3x2L + -3x2L = 10l + 6lx + -5xL + -3x2L

Combine like terms: 3x2L + -3x2L = 0
0 = 10l + 6lx + -5xL + -3x2L

Simplifying
0 = 10l + 6lx + -5xL + -3x2L

The solution to this equation could not be determined.

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

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