(9x+8y)(4y+6x)=

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Solution for (9x+8y)(4y+6x)= equation: 


Simplifying
(9x + 8y)(4y + 6x) = 0

Reorder the terms:
(9x + 8y)(6x + 4y) = 0

Multiply (9x + 8y) * (6x + 4y)
(9x * (6x + 4y) + 8y * (6x + 4y)) = 0
((6x * 9x + 4y * 9x) + 8y * (6x + 4y)) = 0

Reorder the terms:
((36xy + 54x2) + 8y * (6x + 4y)) = 0
((36xy + 54x2) + 8y * (6x + 4y)) = 0
(36xy + 54x2 + (6x * 8y + 4y * 8y)) = 0
(36xy + 54x2 + (48xy + 32y2)) = 0

Reorder the terms:
(36xy + 48xy + 54x2 + 32y2) = 0

Combine like terms: 36xy + 48xy = 84xy
(84xy + 54x2 + 32y2) = 0

Solving
84xy + 54x2 + 32y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(42xy + 27x2 + 16y2) = 0

Factor a trinomial.
2((3x + 2y)(9x + 8y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3x + 2y)' equal to zero and attempt to solve:

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

Add '-2y' to each side of the equation.
3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
3x + 0 = 0 + -2y
3x = 0 + -2y
Remove the zero:
3x = -2y

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y

Subproblem 2
Set the factor '(9x + 8y)' equal to zero and attempt to solve:

Simplifying
9x + 8y = 0

Solving
9x + 8y = 0

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

Add '-8y' to each side of the equation.
9x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
9x + 0 = 0 + -8y
9x = 0 + -8y
Remove the zero:
9x = -8y

Divide each side by '9'.
x = -0.8888888889y

Simplifying
x = -0.8888888889y
Solution
x = {-0.6666666667y, -0.8888888889y}

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