(16x^2+25y^2)(4x+5y)(4x-5y)=0

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Solution for (16x^2+25y^2)(4x+5y)(4x-5y)=0 equation: 


Simplifying
(16x2 + 25y2)(4x + 5y)(4x + -5y) = 0

Multiply (16x2 + 25y2) * (4x + 5y)
(16x2 * (4x + 5y) + 25y2 * (4x + 5y))(4x + -5y) = 0
((4x * 16x2 + 5y * 16x2) + 25y2 * (4x + 5y))(4x + -5y) = 0

Reorder the terms:
((80x2y + 64x3) + 25y2 * (4x + 5y))(4x + -5y) = 0
((80x2y + 64x3) + 25y2 * (4x + 5y))(4x + -5y) = 0
(80x2y + 64x3 + (4x * 25y2 + 5y * 25y2))(4x + -5y) = 0
(80x2y + 64x3 + (100xy2 + 125y3))(4x + -5y) = 0

Reorder the terms:
(100xy2 + 80x2y + 64x3 + 125y3)(4x + -5y) = 0
(100xy2 + 80x2y + 64x3 + 125y3)(4x + -5y) = 0

Multiply (100xy2 + 80x2y + 64x3 + 125y3) * (4x + -5y)
(100xy2 * (4x + -5y) + 80x2y * (4x + -5y) + 64x3 * (4x + -5y) + 125y3 * (4x + -5y)) = 0
((4x * 100xy2 + -5y * 100xy2) + 80x2y * (4x + -5y) + 64x3 * (4x + -5y) + 125y3 * (4x + -5y)) = 0

Reorder the terms:
((-500xy3 + 400x2y2) + 80x2y * (4x + -5y) + 64x3 * (4x + -5y) + 125y3 * (4x + -5y)) = 0
((-500xy3 + 400x2y2) + 80x2y * (4x + -5y) + 64x3 * (4x + -5y) + 125y3 * (4x + -5y)) = 0
(-500xy3 + 400x2y2 + (4x * 80x2y + -5y * 80x2y) + 64x3 * (4x + -5y) + 125y3 * (4x + -5y)) = 0

Reorder the terms:
(-500xy3 + 400x2y2 + (-400x2y2 + 320x3y) + 64x3 * (4x + -5y) + 125y3 * (4x + -5y)) = 0
(-500xy3 + 400x2y2 + (-400x2y2 + 320x3y) + 64x3 * (4x + -5y) + 125y3 * (4x + -5y)) = 0
(-500xy3 + 400x2y2 + -400x2y2 + 320x3y + (4x * 64x3 + -5y * 64x3) + 125y3 * (4x + -5y)) = 0

Reorder the terms:
(-500xy3 + 400x2y2 + -400x2y2 + 320x3y + (-320x3y + 256x4) + 125y3 * (4x + -5y)) = 0
(-500xy3 + 400x2y2 + -400x2y2 + 320x3y + (-320x3y + 256x4) + 125y3 * (4x + -5y)) = 0
(-500xy3 + 400x2y2 + -400x2y2 + 320x3y + -320x3y + 256x4 + (4x * 125y3 + -5y * 125y3)) = 0
(-500xy3 + 400x2y2 + -400x2y2 + 320x3y + -320x3y + 256x4 + (500xy3 + -625y4)) = 0

Reorder the terms:
(-500xy3 + 500xy3 + 400x2y2 + -400x2y2 + 320x3y + -320x3y + 256x4 + -625y4) = 0

Combine like terms: -500xy3 + 500xy3 = 0
(0 + 400x2y2 + -400x2y2 + 320x3y + -320x3y + 256x4 + -625y4) = 0
(400x2y2 + -400x2y2 + 320x3y + -320x3y + 256x4 + -625y4) = 0

Combine like terms: 400x2y2 + -400x2y2 = 0
(0 + 320x3y + -320x3y + 256x4 + -625y4) = 0
(320x3y + -320x3y + 256x4 + -625y4) = 0

Combine like terms: 320x3y + -320x3y = 0
(0 + 256x4 + -625y4) = 0
(256x4 + -625y4) = 0

Solving
256x4 + -625y4 = 0

Solving for variable 'x'.

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

Add '625y4' to each side of the equation.
256x4 + -625y4 + 625y4 = 0 + 625y4

Combine like terms: -625y4 + 625y4 = 0
256x4 + 0 = 0 + 625y4
256x4 = 0 + 625y4
Remove the zero:
256x4 = 625y4

Divide each side by '256'.
x4 = 2.44140625y4

Simplifying
x4 = 2.44140625y4

Combine like terms: 2.44140625y4 + -2.44140625y4 = 0.00000000
x4 + -2.44140625y4 = 0.00000000

Factor a difference between two squares.
(x2 + 1.5625y2)(x2 + -1.5625y2) = 0.00000000

Factor a difference between two squares.
(x2 + 1.5625y2)((x + 1.25y)(x + -1.25y)) = 0.00000000


Subproblem 1
Set the factor '(x2 + 1.5625y2)' equal to zero and attempt to solve:

Simplifying
x2 + 1.5625y2 = 0

Solving
x2 + 1.5625y2 = 0

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

Add '-1.5625y2' to each side of the equation.
x2 + 1.5625y2 + -1.5625y2 = 0 + -1.5625y2

Combine like terms: 1.5625y2 + -1.5625y2 = 0.0000
x2 + 0.0000 = 0 + -1.5625y2
x2 = 0 + -1.5625y2
Remove the zero:
x2 = -1.5625y2

Simplifying
x2 = -1.5625y2

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 '(x + 1.25y)' equal to zero and attempt to solve:

Simplifying
x + 1.25y = 0

Solving
x + 1.25y = 0

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

Add '-1.25y' to each side of the equation.
x + 1.25y + -1.25y = 0 + -1.25y

Combine like terms: 1.25y + -1.25y = 0.00
x + 0.00 = 0 + -1.25y
x = 0 + -1.25y
Remove the zero:
x = -1.25y

Simplifying
x = -1.25y

Subproblem 3
Set the factor '(x + -1.25y)' equal to zero and attempt to solve:

Simplifying
x + -1.25y = 0

Solving
x + -1.25y = 0

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

Add '1.25y' to each side of the equation.
x + -1.25y + 1.25y = 0 + 1.25y

Combine like terms: -1.25y + 1.25y = 0.00
x + 0.00 = 0 + 1.25y
x = 0 + 1.25y
Remove the zero:
x = 1.25y

Simplifying
x = 1.25y
Solution
x = {-1.25y, 1.25y}

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