(3x+5y)(7x-4y)=0

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Solution for (3x+5y)(7x-4y)=0 equation: 


Simplifying
(3x + 5y)(7x + -4y) = 0

Multiply (3x + 5y) * (7x + -4y)
(3x * (7x + -4y) + 5y * (7x + -4y)) = 0
((7x * 3x + -4y * 3x) + 5y * (7x + -4y)) = 0

Reorder the terms:
((-12xy + 21x2) + 5y * (7x + -4y)) = 0
((-12xy + 21x2) + 5y * (7x + -4y)) = 0
(-12xy + 21x2 + (7x * 5y + -4y * 5y)) = 0
(-12xy + 21x2 + (35xy + -20y2)) = 0

Reorder the terms:
(-12xy + 35xy + 21x2 + -20y2) = 0

Combine like terms: -12xy + 35xy = 23xy
(23xy + 21x2 + -20y2) = 0

Solving
23xy + 21x2 + -20y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + -4y)(3x + 5y) = 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 + 5y)' equal to zero and attempt to solve:

Simplifying
3x + 5y = 0

Solving
3x + 5y = 0

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

Add '-5y' to each side of the equation.
3x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
3x + 0 = 0 + -5y
3x = 0 + -5y
Remove the zero:
3x = -5y

Divide each side by '3'.
x = -1.666666667y

Simplifying
x = -1.666666667y
Solution
x = {0.5714285714y, -1.666666667y}

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