(x+3y)(6x-5y)=0

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Solution for (x+3y)(6x-5y)=0 equation: 


Simplifying
(x + 3y)(6x + -5y) = 0

Multiply (x + 3y) * (6x + -5y)
(x(6x + -5y) + 3y * (6x + -5y)) = 0
((6x * x + -5y * x) + 3y * (6x + -5y)) = 0

Reorder the terms:
((-5xy + 6x2) + 3y * (6x + -5y)) = 0
((-5xy + 6x2) + 3y * (6x + -5y)) = 0
(-5xy + 6x2 + (6x * 3y + -5y * 3y)) = 0
(-5xy + 6x2 + (18xy + -15y2)) = 0

Reorder the terms:
(-5xy + 18xy + 6x2 + -15y2) = 0

Combine like terms: -5xy + 18xy = 13xy
(13xy + 6x2 + -15y2) = 0

Solving
13xy + 6x2 + -15y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6x + -5y)(x + 3y) = 0


Subproblem 1
Set the factor '(6x + -5y)' equal to zero and attempt to solve:

Simplifying
6x + -5y = 0

Solving
6x + -5y = 0

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

Add '5y' to each side of the equation.
6x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
6x + 0 = 0 + 5y
6x = 0 + 5y
Remove the zero:
6x = 5y

Divide each side by '6'.
x = 0.8333333333y

Simplifying
x = 0.8333333333y

Subproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

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

Simplifying
x = -3y
Solution
x = {0.8333333333y, -3y}

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