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

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


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

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

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

Combine like terms: 2xy + 15xy = 17xy
17xy + 6x2 + 5y2 = 0

Solving
17xy + 6x2 + 5y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
2x + 5y = 0

Solving
2x + 5y = 0

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

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

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

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y
Solution
x = {-0.3333333333y, -2.5y}

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