4x^2+16xy=9y^2

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Solution for 4x^2+16xy=9y^2 equation: 


Simplifying
4x2 + 16xy = 9y2

Reorder the terms:
16xy + 4x2 = 9y2

Solving
16xy + 4x2 = 9y2

Solving for variable 'x'.

Combine like terms: 9y2 + -9y2 = 0
16xy + 4x2 + -9y2 = 0

Factor a trinomial.
(2x + -1y)(2x + 9y) = 0


Subproblem 1
Set the factor '(2x + -1y)' equal to zero and attempt to solve:

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y

Subproblem 2
Set the factor '(2x + 9y)' equal to zero and attempt to solve:

Simplifying
2x + 9y = 0

Solving
2x + 9y = 0

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

Add '-9y' to each side of the equation.
2x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
2x + 0 = 0 + -9y
2x = 0 + -9y
Remove the zero:
2x = -9y

Divide each side by '2'.
x = -4.5y

Simplifying
x = -4.5y
Solution
x = {0.5y, -4.5y}

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