(lnx-4)(x^2+9x)=0

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Solution for (lnx-4)(x^2+9x)=0 equation: 


Simplifying
(lnx + -4)(x2 + 9x) = 0

Reorder the terms:
(-4 + lnx)(x2 + 9x) = 0

Reorder the terms:
(-4 + lnx)(9x + x2) = 0

Multiply (-4 + lnx) * (9x + x2)
(-4(9x + x2) + lnx(9x + x2)) = 0
((9x * -4 + x2 * -4) + lnx(9x + x2)) = 0
((-36x + -4x2) + lnx(9x + x2)) = 0
(-36x + -4x2 + (9x * lnx + x2 * lnx)) = 0
(-36x + -4x2 + (9lnx2 + lnx3)) = 0

Reorder the terms:
(9lnx2 + lnx3 + -36x + -4x2) = 0
(9lnx2 + lnx3 + -36x + -4x2) = 0

Solving
9lnx2 + lnx3 + -36x + -4x2 = 0

Solving for variable 'l'.

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

Add '36x' to each side of the equation.
9lnx2 + lnx3 + -36x + 36x + -4x2 = 0 + 36x

Combine like terms: -36x + 36x = 0
9lnx2 + lnx3 + 0 + -4x2 = 0 + 36x
9lnx2 + lnx3 + -4x2 = 0 + 36x
Remove the zero:
9lnx2 + lnx3 + -4x2 = 36x

Add '4x2' to each side of the equation.
9lnx2 + lnx3 + -4x2 + 4x2 = 36x + 4x2

Combine like terms: -4x2 + 4x2 = 0
9lnx2 + lnx3 + 0 = 36x + 4x2
9lnx2 + lnx3 = 36x + 4x2

Reorder the terms:
9lnx2 + lnx3 + -36x + -4x2 = 36x + -36x + 4x2 + -4x2

Combine like terms: 36x + -36x = 0
9lnx2 + lnx3 + -36x + -4x2 = 0 + 4x2 + -4x2
9lnx2 + lnx3 + -36x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9lnx2 + lnx3 + -36x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(9lnx + lnx2 + -36 + -4x) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

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 '(9lnx + lnx2 + -36 + -4x)' equal to zero and attempt to solve:

Simplifying
9lnx + lnx2 + -36 + -4x = 0

Reorder the terms:
-36 + 9lnx + lnx2 + -4x = 0

Solving
-36 + 9lnx + lnx2 + -4x = 0

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

Add '36' to each side of the equation.
-36 + 9lnx + lnx2 + 36 + -4x = 0 + 36

Reorder the terms:
-36 + 36 + 9lnx + lnx2 + -4x = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 9lnx + lnx2 + -4x = 0 + 36
9lnx + lnx2 + -4x = 0 + 36

Combine like terms: 0 + 36 = 36
9lnx + lnx2 + -4x = 36

Add '4x' to each side of the equation.
9lnx + lnx2 + -4x + 4x = 36 + 4x

Combine like terms: -4x + 4x = 0
9lnx + lnx2 + 0 = 36 + 4x
9lnx + lnx2 = 36 + 4x

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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