2x^4-4x^3=-3x^2

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


Simplifying
2x4 + -4x3 = -3x2

Reorder the terms:
-4x3 + 2x4 = -3x2

Solving
-4x3 + 2x4 = -3x2

Solving for variable 'x'.

Reorder the terms:
3x2 + -4x3 + 2x4 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
3x2 + -4x3 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(3 + -4x + 2x2) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(3 + -4x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + -4x + 2x2 = 0

Solving
3 + -4x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
1.5 + -2x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -2x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -2x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -2x + x2 = 0 + -1.5
-2x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-2x + x2 = -1.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -1.5 + 1

Reorder the terms:
1 + -2x + x2 = -1.5 + 1

Combine like terms: -1.5 + 1 = -0.5
1 + -2x + x2 = -0.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = -0.5

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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