5x^2-x^3+x=x^2+4x

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Solution for 5x^2-x^3+x=x^2+4x equation: 


Simplifying
5x2 + -1x3 + x = x2 + 4x

Reorder the terms:
x + 5x2 + -1x3 = x2 + 4x

Reorder the terms:
x + 5x2 + -1x3 = 4x + x2

Solving
x + 5x2 + -1x3 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
x + -4x + 5x2 + -1x2 + -1x3 = 4x + x2 + -4x + -1x2

Combine like terms: x + -4x = -3x
-3x + 5x2 + -1x2 + -1x3 = 4x + x2 + -4x + -1x2

Combine like terms: 5x2 + -1x2 = 4x2
-3x + 4x2 + -1x3 = 4x + x2 + -4x + -1x2

Reorder the terms:
-3x + 4x2 + -1x3 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
-3x + 4x2 + -1x3 = 0 + x2 + -1x2
-3x + 4x2 + -1x3 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3x + 4x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + 4x + -1x2) = 0

Factor a trinomial.
x((-3 + x)(1 + -1x)) = 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 '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

Move all terms containing x 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

Simplifying
x = 3

Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 3, 1}

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