(3x-2y)(8x+3y)=

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Solution for (3x-2y)(8x+3y)= equation: 


Simplifying
(3x + -2y)(8x + 3y) = 0

Multiply (3x + -2y) * (8x + 3y)
(3x * (8x + 3y) + -2y * (8x + 3y)) = 0
((8x * 3x + 3y * 3x) + -2y * (8x + 3y)) = 0

Reorder the terms:
((9xy + 24x2) + -2y * (8x + 3y)) = 0
((9xy + 24x2) + -2y * (8x + 3y)) = 0
(9xy + 24x2 + (8x * -2y + 3y * -2y)) = 0
(9xy + 24x2 + (-16xy + -6y2)) = 0

Reorder the terms:
(9xy + -16xy + 24x2 + -6y2) = 0

Combine like terms: 9xy + -16xy = -7xy
(-7xy + 24x2 + -6y2) = 0

Solving
-7xy + 24x2 + -6y2 = 0

Solving for variable 'x'.

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


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 '(8x + 3y)' equal to zero and attempt to solve:

Simplifying
8x + 3y = 0

Solving
8x + 3y = 0

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

Add '-3y' to each side of the equation.
8x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
8x + 0 = 0 + -3y
8x = 0 + -3y
Remove the zero:
8x = -3y

Divide each side by '8'.
x = -0.375y

Simplifying
x = -0.375y
Solution
x = {0.6666666667y, -0.375y}

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