x^2+10xy-75y^2=0

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Solution for x^2+10xy-75y^2=0 equation:


Simplifying
x2 + 10xy + -75y2 = 0

Reorder the terms:
10xy + x2 + -75y2 = 0

Solving
10xy + x2 + -75y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -5y)(x + 15y) = 0

Subproblem 1

Set the factor '(x + -5y)' equal to zero and attempt to solve: Simplifying 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 2

Set the factor '(x + 15y)' equal to zero and attempt to solve: Simplifying x + 15y = 0 Solving x + 15y = 0 Move all terms containing x to the left, all other terms to the right. Add '-15y' to each side of the equation. x + 15y + -15y = 0 + -15y Combine like terms: 15y + -15y = 0 x + 0 = 0 + -15y x = 0 + -15y Remove the zero: x = -15y Simplifying x = -15y

Solution

x = {5y, -15y}

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