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

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Solution for (3x-8y)(x+3y)=0 equation: 


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

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

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

Reorder the terms:
(9xy + -8xy + 3x2 + -24y2) = 0

Combine like terms: 9xy + -8xy = 1xy
(1xy + 3x2 + -24y2) = 0

Solving
1xy + 3x2 + -24y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(3x + -8y)' equal to zero and attempt to solve:

Simplifying
3x + -8y = 0

Solving
3x + -8y = 0

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

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

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

Divide each side by '3'.
x = 2.666666667y

Simplifying
x = 2.666666667y

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 = {2.666666667y, -3y}

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