x^3+3x^2+2x=2x^2+4x

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


Simplifying
x3 + 3x2 + 2x = 2x2 + 4x

Reorder the terms:
2x + 3x2 + x3 = 2x2 + 4x

Reorder the terms:
2x + 3x2 + x3 = 4x + 2x2

Solving
2x + 3x2 + x3 = 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
2x + -4x + 3x2 + -2x2 + x3 = 4x + 2x2 + -4x + -2x2

Combine like terms: 2x + -4x = -2x
-2x + 3x2 + -2x2 + x3 = 4x + 2x2 + -4x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-2x + 1x2 + x3 = 4x + 2x2 + -4x + -2x2

Reorder the terms:
-2x + 1x2 + x3 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
-2x + 1x2 + x3 = 0 + 2x2 + -2x2
-2x + 1x2 + x3 = 2x2 + -2x2

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

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

Factor a trinomial.
x((-2 + -1x)(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 '(-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

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, -2, 1}

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