(2x-7y)(x+y)=

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Solution for (2x-7y)(x+y)= equation: 


Simplifying
(2x + -7y)(x + y) = 0

Multiply (2x + -7y) * (x + y)
(2x * (x + y) + -7y * (x + y)) = 0
((x * 2x + y * 2x) + -7y * (x + y)) = 0

Reorder the terms:
((2xy + 2x2) + -7y * (x + y)) = 0
((2xy + 2x2) + -7y * (x + y)) = 0
(2xy + 2x2 + (x * -7y + y * -7y)) = 0
(2xy + 2x2 + (-7xy + -7y2)) = 0

Reorder the terms:
(2xy + -7xy + 2x2 + -7y2) = 0

Combine like terms: 2xy + -7xy = -5xy
(-5xy + 2x2 + -7y2) = 0

Solving
-5xy + 2x2 + -7y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -7y)(x + y) = 0


Subproblem 1
Set the factor '(2x + -7y)' equal to zero and attempt to solve:

Simplifying
2x + -7y = 0

Solving
2x + -7y = 0

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

Add '7y' to each side of the equation.
2x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
2x + 0 = 0 + 7y
2x = 0 + 7y
Remove the zero:
2x = 7y

Divide each side by '2'.
x = 3.5y

Simplifying
x = 3.5y

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 = {3.5y, -1y}

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