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

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Solution for (2x+7y)(x+y)=0 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 = 9xy
(9xy + 2x2 + 7y2) = 0

Solving
9xy + 2x2 + 7y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-1y, -3.5y}

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