X^2-3x^2-2x=0

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Solution for X^2-3x^2-2x=0 equation: 


Simplifying
X2 + -3x2 + -2x = 0

Reorder the terms:
X2 + -2x + -3x2 = 0

Solving
X2 + -2x + -3x2 = 0

Solving for variable 'X'.

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

Add '2x' to each side of the equation.
X2 + -2x + 2x + -3x2 = 0 + 2x

Combine like terms: -2x + 2x = 0
X2 + 0 + -3x2 = 0 + 2x
X2 + -3x2 = 0 + 2x
Remove the zero:
X2 + -3x2 = 2x

Add '3x2' to each side of the equation.
X2 + -3x2 + 3x2 = 2x + 3x2

Combine like terms: -3x2 + 3x2 = 0
X2 + 0 = 2x + 3x2
X2 = 2x + 3x2

Simplifying
X2 = 2x + 3x2

Reorder the terms:
X2 + -2x + -3x2 = 2x + -2x + 3x2 + -3x2

Combine like terms: 2x + -2x = 0
X2 + -2x + -3x2 = 0 + 3x2 + -3x2
X2 + -2x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
X2 + -2x + -3x2 = 0

Factor a trinomial.
(X + -3x)(X + x) = 0


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

Simplifying
X + -3x = 0

Solving
X + -3x = 0

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

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

Combine like terms: -3x + 3x = 0
X + 0 = 0 + 3x
X = 0 + 3x
Remove the zero:
X = 3x

Simplifying
X = 3x

Subproblem 2
Set the factor '(X + x)' equal to zero and attempt to solve:

Simplifying
X + x = 0

Solving
X + x = 0

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

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

Combine like terms: x + -1x = 0
X + 0 = 0 + -1x
X = 0 + -1x
Remove the zero:
X = -1x

Simplifying
X = -1x
Solution
X = {3x, -1x}

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