(3x-y)(2x+7y)=0

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Solution for (3x-y)(2x+7y)=0 equation: 


Simplifying
(3x + -1y)(2x + 7y) = 0

Multiply (3x + -1y) * (2x + 7y)
(3x * (2x + 7y) + -1y * (2x + 7y)) = 0
((2x * 3x + 7y * 3x) + -1y * (2x + 7y)) = 0

Reorder the terms:
((21xy + 6x2) + -1y * (2x + 7y)) = 0
((21xy + 6x2) + -1y * (2x + 7y)) = 0
(21xy + 6x2 + (2x * -1y + 7y * -1y)) = 0
(21xy + 6x2 + (-2xy + -7y2)) = 0

Reorder the terms:
(21xy + -2xy + 6x2 + -7y2) = 0

Combine like terms: 21xy + -2xy = 19xy
(19xy + 6x2 + -7y2) = 0

Solving
19xy + 6x2 + -7y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -1y)(2x + 7y) = 0


Subproblem 1
Set the factor '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y

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 = {0.3333333333y, -3.5y}

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