x*x+4xy-21y*y=0

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Solution for x*x+4xy-21y*y=0 equation: 


Simplifying
x * x + 4xy + -21y * y = 0

Multiply x * x
x2 + 4xy + -21y * y = 0

Multiply y * y
x2 + 4xy + -21y2 = 0

Reorder the terms:
4xy + x2 + -21y2 = 0

Solving
4xy + x2 + -21y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -3y)(x + 7y) = 0


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

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

Add '3y' to each side of the equation.
x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
x + 0 = 0 + 3y
x = 0 + 3y
Remove the zero:
x = 3y

Simplifying
x = 3y

Subproblem 2
Set the factor '(x + 7y)' equal to zero and attempt to solve:

Simplifying
x + 7y = 0

Solving
x + 7y = 0

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

Add '-7y' to each side of the equation.
x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
x + 0 = 0 + -7y
x = 0 + -7y
Remove the zero:
x = -7y

Simplifying
x = -7y
Solution
x = {3y, -7y}

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