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

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


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

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

Reorder the terms:
((-49xy + -7x2) + y(x + 7y)) = 0
((-49xy + -7x2) + y(x + 7y)) = 0
(-49xy + -7x2 + (x * y + 7y * y)) = 0
(-49xy + -7x2 + (xy + 7y2)) = 0

Reorder the terms:
(-49xy + xy + -7x2 + 7y2) = 0

Combine like terms: -49xy + xy = -48xy
(-48xy + -7x2 + 7y2) = 0

Solving
-48xy + -7x2 + 7y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1x + -7y)(7x + -1y) = 0


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

Simplifying
-1x + -7y = 0

Solving
-1x + -7y = 0

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

Add '7y' to each side of the equation.
-1x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
-1x + 0 = 0 + 7y
-1x = 0 + 7y
Remove the zero:
-1x = 7y

Divide each side by '-1'.
x = -7y

Simplifying
x = -7y

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

Simplifying
7x + -1y = 0

Solving
7x + -1y = 0

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

Add 'y' to each side of the equation.
7x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
7x + 0 = 0 + y
7x = 0 + y
Remove the zero:
7x = y

Divide each side by '7'.
x = 0.1428571429y

Simplifying
x = 0.1428571429y
Solution
x = {-7y, 0.1428571429y}

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