(7x+3y)(2x-4y)=

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Solution for (7x+3y)(2x-4y)= equation: 


Simplifying
(7x + 3y)(2x + -4y) = 0

Multiply (7x + 3y) * (2x + -4y)
(7x * (2x + -4y) + 3y * (2x + -4y)) = 0
((2x * 7x + -4y * 7x) + 3y * (2x + -4y)) = 0

Reorder the terms:
((-28xy + 14x2) + 3y * (2x + -4y)) = 0
((-28xy + 14x2) + 3y * (2x + -4y)) = 0
(-28xy + 14x2 + (2x * 3y + -4y * 3y)) = 0
(-28xy + 14x2 + (6xy + -12y2)) = 0

Reorder the terms:
(-28xy + 6xy + 14x2 + -12y2) = 0

Combine like terms: -28xy + 6xy = -22xy
(-22xy + 14x2 + -12y2) = 0

Solving
-22xy + 14x2 + -12y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-11xy + 7x2 + -6y2) = 0

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

Ignore the factor 2.

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

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

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

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

Simplifying
x = 2y

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

Simplifying
7x + 3y = 0

Solving
7x + 3y = 0

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

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

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

Divide each side by '7'.
x = -0.4285714286y

Simplifying
x = -0.4285714286y
Solution
x = {2y, -0.4285714286y}

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