2x^3+13x=8x^2

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Solution for 2x^3+13x=8x^2 equation: 


Simplifying
2x3 + 13x = 8x2

Reorder the terms:
13x + 2x3 = 8x2

Solving
13x + 2x3 = 8x2

Solving for variable 'x'.

Reorder the terms:
13x + -8x2 + 2x3 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
13x + -8x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + -8x + 2x2) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(13 + -8x + 2x2)' equal to zero and attempt to solve:

Simplifying
13 + -8x + 2x2 = 0

Solving
13 + -8x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
6.5 + -4x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -4x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -4x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -4x + x2 = 0 + -6.5
-4x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-4x + x2 = -6.5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -6.5 + 4

Reorder the terms:
4 + -4x + x2 = -6.5 + 4

Combine like terms: -6.5 + 4 = -2.5
4 + -4x + x2 = -2.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = -2.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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