5x^2+4xy-33y^2=0

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Solution for 5x^2+4xy-33y^2=0 equation: 


Simplifying
5x2 + 4xy + -33y2 = 0

Reorder the terms:
4xy + 5x2 + -33y2 = 0

Solving
4xy + 5x2 + -33y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -11y)(x + 3y) = 0


Subproblem 1
Set the factor '(5x + -11y)' equal to zero and attempt to solve:

Simplifying
5x + -11y = 0

Solving
5x + -11y = 0

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

Add '11y' to each side of the equation.
5x + -11y + 11y = 0 + 11y

Combine like terms: -11y + 11y = 0
5x + 0 = 0 + 11y
5x = 0 + 11y
Remove the zero:
5x = 11y

Divide each side by '5'.
x = 2.2y

Simplifying
x = 2.2y

Subproblem 2
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
Solution
x = {2.2y, -3y}

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