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

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


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

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

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

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

Combine like terms: 10xy + 3xy = 13xy
(13xy + 15x2 + 2y2) = 0

Solving
13xy + 15x2 + 2y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.2y, -0.6666666667y}

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