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

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


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

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

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

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

Combine like terms: 6xy + -5xy = 1xy
(1xy + 6x2 + -5y2) = 0

Solving
1xy + 6x2 + -5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6x + -5y)(x + y) = 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 + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {0.8333333333y, -1y}

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