(x+3)*(x-3)*lnx=0

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Solution for (x+3)*(x-3)*lnx=0 equation:


Simplifying
(x + 3)(x + -3) * lnx = 0

Reorder the terms:
(3 + x)(x + -3) * lnx = 0

Reorder the terms:
(3 + x)(-3 + x) * lnx = 0

Reorder the terms for easier multiplication:
lnx(3 + x)(-3 + x) = 0

Multiply (3 + x) * (-3 + x)
lnx(3(-3 + x) + x(-3 + x)) = 0
lnx((-3 * 3 + x * 3) + x(-3 + x)) = 0
lnx((-9 + 3x) + x(-3 + x)) = 0
lnx(-9 + 3x + (-3 * x + x * x)) = 0
lnx(-9 + 3x + (-3x + x2)) = 0

Combine like terms: 3x + -3x = 0
lnx(-9 + 0 + x2) = 0
lnx(-9 + x2) = 0
(-9 * lnx + x2 * lnx) = 0
(-9lnx + lnx3) = 0

Solving
-9lnx + lnx3 = 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), 'lnx'.
lnx(-9 + x2) = 0

Factor a difference between two squares.
lnx((3 + x)(-3 + x)) = 0

Subproblem 1

Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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