ln(2x+5)*ln(-x-3)=0

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Solution for ln(2x+5)*ln(-x-3)=0 equation:


Simplifying
ln(2x + 5) * ln(-1x + -3) = 0

Reorder the terms:
ln(5 + 2x) * ln(-1x + -3) = 0

Reorder the terms:
ln(5 + 2x) * ln(-3 + -1x) = 0

Reorder the terms for easier multiplication:
ln * ln(5 + 2x)(-3 + -1x) = 0

Multiply ln * ln
l2n2(5 + 2x)(-3 + -1x) = 0

Multiply (5 + 2x) * (-3 + -1x)
l2n2(5(-3 + -1x) + 2x * (-3 + -1x)) = 0
l2n2((-3 * 5 + -1x * 5) + 2x * (-3 + -1x)) = 0
l2n2((-15 + -5x) + 2x * (-3 + -1x)) = 0
l2n2(-15 + -5x + (-3 * 2x + -1x * 2x)) = 0
l2n2(-15 + -5x + (-6x + -2x2)) = 0

Combine like terms: -5x + -6x = -11x
l2n2(-15 + -11x + -2x2) = 0
(-15 * l2n2 + -11x * l2n2 + -2x2 * l2n2) = 0
(-15l2n2 + -11l2n2x + -2l2n2x2) = 0

Solving
-15l2n2 + -11l2n2x + -2l2n2x2 = 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), '-1l2n2'.
-1l2n2(15 + 11x + 2x2) = 0

Factor a trinomial.
-1l2n2((3 + x)(5 + 2x)) = 0

Ignore the factor -1.

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 '(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 '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Add '-2x' to each side of the equation. 2x + -2x = -5 + -2x Combine like terms: 2x + -2x = 0 0 = -5 + -2x Simplifying 0 = -5 + -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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