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

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


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

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

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

Reorder the terms:
(3xy + -10xy + 15x2 + -2y2) = 0

Combine like terms: 3xy + -10xy = -7xy
(-7xy + 15x2 + -2y2) = 0

Solving
-7xy + 15x2 + -2y2 = 0

Solving for variable 'x'.

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

Simplifying
5x + y = 0

Solving
5x + y = 0

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

Add '-1y' to each side of the equation.
5x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
5x + 0 = 0 + -1y
5x = 0 + -1y
Remove the zero:
5x = -1y

Divide each side by '5'.
x = -0.2y

Simplifying
x = -0.2y
Solution
x = {0.6666666667y, -0.2y}

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