(3x+7y)(-7x-y)=0

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Solution for (3x+7y)(-7x-y)=0 equation: 


Simplifying
(3x + 7y)(-7x + -1y) = 0

Multiply (3x + 7y) * (-7x + -1y)
(3x * (-7x + -1y) + 7y * (-7x + -1y)) = 0
((-7x * 3x + -1y * 3x) + 7y * (-7x + -1y)) = 0

Reorder the terms:
((-3xy + -21x2) + 7y * (-7x + -1y)) = 0
((-3xy + -21x2) + 7y * (-7x + -1y)) = 0
(-3xy + -21x2 + (-7x * 7y + -1y * 7y)) = 0
(-3xy + -21x2 + (-49xy + -7y2)) = 0

Reorder the terms:
(-3xy + -49xy + -21x2 + -7y2) = 0

Combine like terms: -3xy + -49xy = -52xy
(-52xy + -21x2 + -7y2) = 0

Solving
-52xy + -21x2 + -7y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(52xy + 21x2 + 7y2) = 0

Factor a trinomial.
-1((7x + y)(3x + 7y)) = 0

Ignore the factor -1.

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

Simplifying
7x + y = 0

Solving
7x + y = 0

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

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

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

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

Simplifying
x = -0.1428571429y

Subproblem 2
Set the factor '(3x + 7y)' equal to zero and attempt to solve:

Simplifying
3x + 7y = 0

Solving
3x + 7y = 0

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

Add '-7y' to each side of the equation.
3x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
3x + 0 = 0 + -7y
3x = 0 + -7y
Remove the zero:
3x = -7y

Divide each side by '3'.
x = -2.333333333y

Simplifying
x = -2.333333333y
Solution
x = {-0.1428571429y, -2.333333333y}

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