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

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


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

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

Reorder the terms:
((7xy + 2x2) + -3y * (2x + 7y)) = 0
((7xy + 2x2) + -3y * (2x + 7y)) = 0
(7xy + 2x2 + (2x * -3y + 7y * -3y)) = 0
(7xy + 2x2 + (-6xy + -21y2)) = 0

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

Combine like terms: 7xy + -6xy = 1xy
(1xy + 2x2 + -21y2) = 0

Solving
1xy + 2x2 + -21y2 = 0

Solving for variable 'x'.

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


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

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

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

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

Simplifying
x = 3y

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 = {3y, -3.5y}

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