(5x-2y)(3x+4y)=0

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Solution for (5x-2y)(3x+4y)=0 equation: 


Simplifying
(5x + -2y)(3x + 4y) = 0

Multiply (5x + -2y) * (3x + 4y)
(5x * (3x + 4y) + -2y * (3x + 4y)) = 0
((3x * 5x + 4y * 5x) + -2y * (3x + 4y)) = 0

Reorder the terms:
((20xy + 15x2) + -2y * (3x + 4y)) = 0
((20xy + 15x2) + -2y * (3x + 4y)) = 0
(20xy + 15x2 + (3x * -2y + 4y * -2y)) = 0
(20xy + 15x2 + (-6xy + -8y2)) = 0

Reorder the terms:
(20xy + -6xy + 15x2 + -8y2) = 0

Combine like terms: 20xy + -6xy = 14xy
(14xy + 15x2 + -8y2) = 0

Solving
14xy + 15x2 + -8y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -2y)(3x + 4y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3x + 4y)' equal to zero and attempt to solve:

Simplifying
3x + 4y = 0

Solving
3x + 4y = 0

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

Add '-4y' to each side of the equation.
3x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
3x + 0 = 0 + -4y
3x = 0 + -4y
Remove the zero:
3x = -4y

Divide each side by '3'.
x = -1.333333333y

Simplifying
x = -1.333333333y
Solution
x = {0.4y, -1.333333333y}

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