5x^4y^2(2x^2-5xy+3y^2)=

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Solution for 5x^4y^2(2x^2-5xy+3y^2)= equation: 


Simplifying
5x4y2(2x2 + -5xy + 3y2) = 0

Reorder the terms:
5x4y2(-5xy + 2x2 + 3y2) = 0
(-5xy * 5x4y2 + 2x2 * 5x4y2 + 3y2 * 5x4y2) = 0

Reorder the terms:
(15x4y4 + -25x5y3 + 10x6y2) = 0
(15x4y4 + -25x5y3 + 10x6y2) = 0

Solving
15x4y4 + -25x5y3 + 10x6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x4y2'.
5x4y2(3y2 + -5xy + 2x2) = 0

Factor a trinomial.
5x4y2((y + -1x)(3y + -2x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'x4y2' equal to zero and attempt to solve:

Simplifying
x4y2 = 0

Solving
x4y2 = 0

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

Simplifying
x4y2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
y + -1x = 0

Reorder the terms:
-1x + y = 0

Solving
-1x + y = 0

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

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

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

Divide each side by '-1'.
x = y

Simplifying
x = y

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

Simplifying
3y + -2x = 0

Reorder the terms:
-2x + 3y = 0

Solving
-2x + 3y = 0

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

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

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

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

Simplifying
x = 1.5y
Solution
x = {y, 1.5y}

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