(x^2+7xy-4y^2)(5x^2+3xy)=0

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Solution for (x^2+7xy-4y^2)(5x^2+3xy)=0 equation: 


Simplifying
(x2 + 7xy + -4y2)(5x2 + 3xy) = 0

Reorder the terms:
(7xy + x2 + -4y2)(5x2 + 3xy) = 0

Reorder the terms:
(7xy + x2 + -4y2)(3xy + 5x2) = 0

Multiply (7xy + x2 + -4y2) * (3xy + 5x2)
(7xy * (3xy + 5x2) + x2(3xy + 5x2) + -4y2 * (3xy + 5x2)) = 0
((3xy * 7xy + 5x2 * 7xy) + x2(3xy + 5x2) + -4y2 * (3xy + 5x2)) = 0
((21x2y2 + 35x3y) + x2(3xy + 5x2) + -4y2 * (3xy + 5x2)) = 0
(21x2y2 + 35x3y + (3xy * x2 + 5x2 * x2) + -4y2 * (3xy + 5x2)) = 0
(21x2y2 + 35x3y + (3x3y + 5x4) + -4y2 * (3xy + 5x2)) = 0
(21x2y2 + 35x3y + 3x3y + 5x4 + (3xy * -4y2 + 5x2 * -4y2)) = 0
(21x2y2 + 35x3y + 3x3y + 5x4 + (-12xy3 + -20x2y2)) = 0

Reorder the terms:
(-12xy3 + 21x2y2 + -20x2y2 + 35x3y + 3x3y + 5x4) = 0

Combine like terms: 21x2y2 + -20x2y2 = 1x2y2
(-12xy3 + 1x2y2 + 35x3y + 3x3y + 5x4) = 0

Combine like terms: 35x3y + 3x3y = 38x3y
(-12xy3 + 1x2y2 + 38x3y + 5x4) = 0

Solving
-12xy3 + 1x2y2 + 38x3y + 5x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-12y3 + xy2 + 38x2y + 5x3) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-12y3 + xy2 + 38x2y + 5x3)' equal to zero and attempt to solve:

Simplifying
-12y3 + xy2 + 38x2y + 5x3 = 0

Reorder the terms:
xy2 + 38x2y + 5x3 + -12y3 = 0

Solving
xy2 + 38x2y + 5x3 + -12y3 = 0

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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