10x=3x^2-x^3

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Solution for 10x=3x^2-x^3 equation: 


Simplifying
10x = 3x2 + -1x3

Solving
10x = 3x2 + -1x3

Solving for variable 'x'.

Reorder the terms:
10x + -3x2 + x3 = 3x2 + -3x2 + -1x3 + x3

Combine like terms: 3x2 + -3x2 = 0
10x + -3x2 + x3 = 0 + -1x3 + x3
10x + -3x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
10x + -3x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + -3x + x2) = 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 '(10 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
10 + -3x + x2 = 0

Solving
10 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -3x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -3x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x + x2 = 0 + -10
-3x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-3x + x2 = -10

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -10 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + -3x + x2 = -7.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -7.75

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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