(x^2)(2lnx+5)-3x(x(2lnx+3))+4y=0

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Solution for (x^2)(2lnx+5)-3x(x(2lnx+3))+4y=0 equation:


Simplifying
(x2)(2lnx + 5) + -3x(x(2lnx + 3)) + 4y = 0

Reorder the terms:
x2(5 + 2lnx) + -3x(x(2lnx + 3)) + 4y = 0
(5 * x2 + 2lnx * x2) + -3x(x(2lnx + 3)) + 4y = 0

Reorder the terms:
(2lnx3 + 5x2) + -3x(x(2lnx + 3)) + 4y = 0
(2lnx3 + 5x2) + -3x(x(2lnx + 3)) + 4y = 0

Reorder the terms:
2lnx3 + 5x2 + -3x(x(3 + 2lnx)) + 4y = 0
2lnx3 + 5x2 + -3x((3 * x + 2lnx * x)) + 4y = 0

Reorder the terms:
2lnx3 + 5x2 + -3x((2lnx2 + 3x)) + 4y = 0
2lnx3 + 5x2 + -3x((2lnx2 + 3x)) + 4y = 0
2lnx3 + 5x2 + (2lnx2 * -3x + 3x * -3x) + 4y = 0
2lnx3 + 5x2 + (-6lnx3 + -9x2) + 4y = 0

Reorder the terms:
2lnx3 + -6lnx3 + 5x2 + -9x2 + 4y = 0

Combine like terms: 2lnx3 + -6lnx3 = -4lnx3
-4lnx3 + 5x2 + -9x2 + 4y = 0

Combine like terms: 5x2 + -9x2 = -4x2
-4lnx3 + -4x2 + 4y = 0

Solving
-4lnx3 + -4x2 + 4y = 0

Solving for variable 'l'.

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

Add '4x2' to each side of the equation.
-4lnx3 + -4x2 + 4x2 + 4y = 0 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-4lnx3 + 0 + 4y = 0 + 4x2
-4lnx3 + 4y = 0 + 4x2
Remove the zero:
-4lnx3 + 4y = 4x2

Add '-4y' to each side of the equation.
-4lnx3 + 4y + -4y = 4x2 + -4y

Combine like terms: 4y + -4y = 0
-4lnx3 + 0 = 4x2 + -4y
-4lnx3 = 4x2 + -4y

Divide each side by '-4nx3'.
l = -1n-1x-1 + n-1x-3y

Simplifying
l = -1n-1x-1 + n-1x-3y

Reorder the terms:
l = n-1x-3y + -1n-1x-1

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