5x^2(x^2+2xy-8y^2)=

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Solution for 5x^2(x^2+2xy-8y^2)= equation: 


Simplifying
5x2(x2 + 2xy + -8y2) = 0

Reorder the terms:
5x2(2xy + x2 + -8y2) = 0
(2xy * 5x2 + x2 * 5x2 + -8y2 * 5x2) = 0

Reorder the terms:
(-40x2y2 + 10x3y + 5x4) = 0
(-40x2y2 + 10x3y + 5x4) = 0

Solving
-40x2y2 + 10x3y + 5x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(-8y2 + 2xy + x2) = 0

Factor a trinomial.
5x2((-4y + -1x)(2y + -1x)) = 0

Ignore the factor 5.

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 '(-4y + -1x)' equal to zero and attempt to solve:

Simplifying
-4y + -1x = 0

Reorder the terms:
-1x + -4y = 0

Solving
-1x + -4y = 0

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

Add '4y' to each side of the equation.
-1x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
-1x + 0 = 0 + 4y
-1x = 0 + 4y
Remove the zero:
-1x = 4y

Divide each side by '-1'.
x = -4y

Simplifying
x = -4y

Subproblem 3
Set the factor '(2y + -1x)' equal to zero and attempt to solve:

Simplifying
2y + -1x = 0

Reorder the terms:
-1x + 2y = 0

Solving
-1x + 2y = 0

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

Add '-2y' to each side of the equation.
-1x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-1x + 0 = 0 + -2y
-1x = 0 + -2y
Remove the zero:
-1x = -2y

Divide each side by '-1'.
x = 2y

Simplifying
x = 2y
Solution
x = {0, -4y, 2y}

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