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

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


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

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

Reorder the terms:
((14xy + 21x2) + -4y * (3x + 2y)) = 0
((14xy + 21x2) + -4y * (3x + 2y)) = 0
(14xy + 21x2 + (3x * -4y + 2y * -4y)) = 0
(14xy + 21x2 + (-12xy + -8y2)) = 0

Reorder the terms:
(14xy + -12xy + 21x2 + -8y2) = 0

Combine like terms: 14xy + -12xy = 2xy
(2xy + 21x2 + -8y2) = 0

Solving
2xy + 21x2 + -8y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + -4y)(3x + 2y) = 0


Subproblem 1
Set the factor '(7x + -4y)' equal to zero and attempt to solve:

Simplifying
7x + -4y = 0

Solving
7x + -4y = 0

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

Add '4y' to each side of the equation.
7x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
7x + 0 = 0 + 4y
7x = 0 + 4y
Remove the zero:
7x = 4y

Divide each side by '7'.
x = 0.5714285714y

Simplifying
x = 0.5714285714y

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

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

Add '-2y' to each side of the equation.
3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
3x + 0 = 0 + -2y
3x = 0 + -2y
Remove the zero:
3x = -2y

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y
Solution
x = {0.5714285714y, -0.6666666667y}

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