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

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


Simplifying
X2 + 2x2 + -3x = 0

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

Solving
X2 + -3x + 2x2 = 0

Solving for variable 'X'.

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

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

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

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

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

Simplifying
X2 = 3x + -2x2

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

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

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

Factor a trinomial.
(X + -2x)(X + -1x) = 0


Subproblem 1
Set the factor '(X + -2x)' equal to zero and attempt to solve:

Simplifying
X + -2x = 0

Solving
X + -2x = 0

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

Add '2x' to each side of the equation.
X + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
X + 0 = 0 + 2x
X = 0 + 2x
Remove the zero:
X = 2x

Simplifying
X = 2x

Subproblem 2
Set the factor '(X + -1x)' equal to zero and attempt to solve:

Simplifying
X + -1x = 0

Solving
X + -1x = 0

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

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

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

Simplifying
X = x
Solution
X = {2x, x}

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