x^2+7xy-8y^2=0

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Solution for x^2+7xy-8y^2=0 equation: 


Simplifying
x2 + 7xy + -8y2 = 0

Reorder the terms:
7xy + x2 + -8y2 = 0

Solving
7xy + x2 + -8y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y)(x + 8y) = 0


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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y

Subproblem 2
Set the factor '(x + 8y)' equal to zero and attempt to solve:

Simplifying
x + 8y = 0

Solving
x + 8y = 0

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

Add '-8y' to each side of the equation.
x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
x + 0 = 0 + -8y
x = 0 + -8y
Remove the zero:
x = -8y

Simplifying
x = -8y
Solution
x = {y, -8y}

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