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

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


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

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

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

Reorder the terms:
(5xy + -6xy + 15x2 + -2y2) = 0

Combine like terms: 5xy + -6xy = -1xy
(-1xy + 15x2 + -2y2) = 0

Solving
-1xy + 15x2 + -2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -2y)(3x + y) = 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 + y)' equal to zero and attempt to solve:

Simplifying
3x + y = 0

Solving
3x + y = 0

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

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y
Solution
x = {0.4y, -0.3333333333y}

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