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

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


Simplifying
(5x + 2y)(3x + -1y) = 0

Multiply (5x + 2y) * (3x + -1y)
(5x * (3x + -1y) + 2y * (3x + -1y)) = 0
((3x * 5x + -1y * 5x) + 2y * (3x + -1y)) = 0

Reorder the terms:
((-5xy + 15x2) + 2y * (3x + -1y)) = 0
((-5xy + 15x2) + 2y * (3x + -1y)) = 0
(-5xy + 15x2 + (3x * 2y + -1y * 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.
(3x + -1y)(5x + 2y) = 0


Subproblem 1
Set the factor '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

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

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

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

Simplifying
x = 0.3333333333y

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 = {0.3333333333y, -0.4y}

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