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

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


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

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

Reorder the terms:
((14xy + 6x2) + -1y * (3x + 7y)) = 0
((14xy + 6x2) + -1y * (3x + 7y)) = 0
(14xy + 6x2 + (3x * -1y + 7y * -1y)) = 0
(14xy + 6x2 + (-3xy + -7y2)) = 0

Reorder the terms:
(14xy + -3xy + 6x2 + -7y2) = 0

Combine like terms: 14xy + -3xy = 11xy
(11xy + 6x2 + -7y2) = 0

Solving
11xy + 6x2 + -7y2 = 0

Solving for variable 'x'.

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


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

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y

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 = {0.5y, -2.333333333y}

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