2x^2+ln(2x+5)=x^3+ln(2x+5)

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

Simplifying
2x2 + ln(2x + 5) = x3 + ln(2x + 5)

Reorder the terms:
2x2 + ln(5 + 2x) = x3 + ln(2x + 5)
2x2 + (5 * ln + 2x * ln) = x3 + ln(2x + 5)
2x2 + (5ln + 2lnx) = x3 + ln(2x + 5)

Reorder the terms:
5ln + 2lnx + 2x2 = x3 + ln(2x + 5)

Reorder the terms:
5ln + 2lnx + 2x2 = x3 + ln(5 + 2x)
5ln + 2lnx + 2x2 = x3 + (5 * ln + 2x * ln)
5ln + 2lnx + 2x2 = x3 + (5ln + 2lnx)

Reorder the terms:
5ln + 2lnx + 2x2 = 5ln + 2lnx + x3

Add '-5ln' to each side of the equation.
5ln + 2lnx + -5ln + 2x2 = 5ln + 2lnx + -5ln + x3

Reorder the terms:
5ln + -5ln + 2lnx + 2x2 = 5ln + 2lnx + -5ln + x3

Combine like terms: 5ln + -5ln = 0
0 + 2lnx + 2x2 = 5ln + 2lnx + -5ln + x3
2lnx + 2x2 = 5ln + 2lnx + -5ln + x3

Reorder the terms:
2lnx + 2x2 = 5ln + -5ln + 2lnx + x3

Combine like terms: 5ln + -5ln = 0
2lnx + 2x2 = 0 + 2lnx + x3
2lnx + 2x2 = 2lnx + x3

Add '-2lnx' to each side of the equation.
2lnx + -2lnx + 2x2 = 2lnx + -2lnx + x3

Combine like terms: 2lnx + -2lnx = 0
0 + 2x2 = 2lnx + -2lnx + x3
2x2 = 2lnx + -2lnx + x3

Combine like terms: 2lnx + -2lnx = 0
2x2 = 0 + x3
2x2 = x3

Solving
2x2 = x3

Solving for variable 'x'.

Combine like terms: x3 + -1x3 = 0
2x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(2 + -1x) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 2}