(2x-3y)(5x+2y)=0

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Solution for (2x-3y)(5x+2y)=0 equation: 


Simplifying
(2x + -3y)(5x + 2y) = 0

Multiply (2x + -3y) * (5x + 2y)
(2x * (5x + 2y) + -3y * (5x + 2y)) = 0
((5x * 2x + 2y * 2x) + -3y * (5x + 2y)) = 0

Reorder the terms:
((4xy + 10x2) + -3y * (5x + 2y)) = 0
((4xy + 10x2) + -3y * (5x + 2y)) = 0
(4xy + 10x2 + (5x * -3y + 2y * -3y)) = 0
(4xy + 10x2 + (-15xy + -6y2)) = 0

Reorder the terms:
(4xy + -15xy + 10x2 + -6y2) = 0

Combine like terms: 4xy + -15xy = -11xy
(-11xy + 10x2 + -6y2) = 0

Solving
-11xy + 10x2 + -6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -3y)(5x + 2y) = 0


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

Simplifying
2x + -3y = 0

Solving
2x + -3y = 0

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

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

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

Divide each side by '2'.
x = 1.5y

Simplifying
x = 1.5y

Subproblem 2
Set the factor '(5x + 2y)' equal to zero and attempt to solve:

Simplifying
5x + 2y = 0

Solving
5x + 2y = 0

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

Add '-2y' to each side of the equation.
5x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
5x + 0 = 0 + -2y
5x = 0 + -2y
Remove the zero:
5x = -2y

Divide each side by '5'.
x = -0.4y

Simplifying
x = -0.4y
Solution
x = {1.5y, -0.4y}

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