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

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Solution for (7x-2y)(x+y)=0 equation: 


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

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

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

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

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

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

Solving for variable 'x'.

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


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

Simplifying
7x + -2y = 0

Solving
7x + -2y = 0

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

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

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

Divide each side by '7'.
x = 0.2857142857y

Simplifying
x = 0.2857142857y

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 = {0.2857142857y, -1y}

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