(9x+2y)(8x-4y)=

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Solution for (9x+2y)(8x-4y)= equation: 


Simplifying
(9x + 2y)(8x + -4y) = 0

Multiply (9x + 2y) * (8x + -4y)
(9x * (8x + -4y) + 2y * (8x + -4y)) = 0
((8x * 9x + -4y * 9x) + 2y * (8x + -4y)) = 0

Reorder the terms:
((-36xy + 72x2) + 2y * (8x + -4y)) = 0
((-36xy + 72x2) + 2y * (8x + -4y)) = 0
(-36xy + 72x2 + (8x * 2y + -4y * 2y)) = 0
(-36xy + 72x2 + (16xy + -8y2)) = 0

Reorder the terms:
(-36xy + 16xy + 72x2 + -8y2) = 0

Combine like terms: -36xy + 16xy = -20xy
(-20xy + 72x2 + -8y2) = 0

Solving
-20xy + 72x2 + -8y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5xy + 18x2 + -2y2) = 0

Factor a trinomial.
4((2x + -1y)(9x + 2y)) = 0

Ignore the factor 4.

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 '(9x + 2y)' equal to zero and attempt to solve:

Simplifying
9x + 2y = 0

Solving
9x + 2y = 0

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

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

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

Divide each side by '9'.
x = -0.2222222222y

Simplifying
x = -0.2222222222y
Solution
x = {0.5y, -0.2222222222y}

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