4x^4+12x^3y^2+9x^2y^4=

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Solution for 4x^4+12x^3y^2+9x^2y^4= equation: 


Simplifying
4x4 + 12x3y2 + 9x2y4 = 0

Reorder the terms:
9x2y4 + 12x3y2 + 4x4 = 0

Solving
9x2y4 + 12x3y2 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(9y4 + 12xy2 + 4x2) = 0

Factor a trinomial.
x2((3y2 + 2x)(3y2 + 2x)) = 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 '(3y2 + 2x)' equal to zero and attempt to solve:

Simplifying
3y2 + 2x = 0

Reorder the terms:
2x + 3y2 = 0

Solving
2x + 3y2 = 0

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

Add '-3y2' to each side of the equation.
2x + 3y2 + -3y2 = 0 + -3y2

Combine like terms: 3y2 + -3y2 = 0
2x + 0 = 0 + -3y2
2x = 0 + -3y2
Remove the zero:
2x = -3y2

Divide each side by '2'.
x = -1.5y2

Simplifying
x = -1.5y2

Subproblem 3
Set the factor '(3y2 + 2x)' equal to zero and attempt to solve:

Simplifying
3y2 + 2x = 0

Reorder the terms:
2x + 3y2 = 0

Solving
2x + 3y2 = 0

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

Add '-3y2' to each side of the equation.
2x + 3y2 + -3y2 = 0 + -3y2

Combine like terms: 3y2 + -3y2 = 0
2x + 0 = 0 + -3y2
2x = 0 + -3y2
Remove the zero:
2x = -3y2

Divide each side by '2'.
x = -1.5y2

Simplifying
x = -1.5y2
Solution
x = {0, -1.5y2, -1.5y2}

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