15x(5x+2y)-y(5x+2y)=0

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Solution for 15x(5x+2y)-y(5x+2y)=0 equation: 


Simplifying
15x(5x + 2y) + -1y(5x + 2y) = 0
(5x * 15x + 2y * 15x) + -1y(5x + 2y) = 0

Reorder the terms:
(30xy + 75x2) + -1y(5x + 2y) = 0
(30xy + 75x2) + -1y(5x + 2y) = 0
30xy + 75x2 + (5x * -1y + 2y * -1y) = 0
30xy + 75x2 + (-5xy + -2y2) = 0

Reorder the terms:
30xy + -5xy + 75x2 + -2y2 = 0

Combine like terms: 30xy + -5xy = 25xy
25xy + 75x2 + -2y2 = 0

Solving
25xy + 75x2 + -2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(15x + -1y)(5x + 2y) = 0


Subproblem 1
Set the factor '(15x + -1y)' equal to zero and attempt to solve:

Simplifying
15x + -1y = 0

Solving
15x + -1y = 0

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

Add 'y' to each side of the equation.
15x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
15x + 0 = 0 + y
15x = 0 + y
Remove the zero:
15x = y

Divide each side by '15'.
x = 0.06666666667y

Simplifying
x = 0.06666666667y

Subproblem 2
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
Solution
x = {0.06666666667y, -0.4y}

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