10x^3-250xy^2=0

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Solution for 10x^3-250xy^2=0 equation:


Simplifying
10x3 + -250xy2 = 0

Reorder the terms:
-250xy2 + 10x3 = 0

Solving
-250xy2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10x'.
10x(-25y2 + x2) = 0

Factor a difference between two squares.
10x((5y + x)(-5y + x)) = 0

Ignore the factor 10.

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 '(5y + x)' equal to zero and attempt to solve: Simplifying 5y + x = 0 Reorder the terms: x + 5y = 0 Solving x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 x + 0 = 0 + -5y x = 0 + -5y Remove the zero: x = -5y Simplifying x = -5y

Subproblem 3

Set the factor '(-5y + x)' equal to zero and attempt to solve: Simplifying -5y + x = 0 Reorder the terms: x + -5y = 0 Solving x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 x + 0 = 0 + 5y x = 0 + 5y Remove the zero: x = 5y Simplifying x = 5y

Solution

x = {0, -5y, 5y}

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