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

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


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

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

Reorder the terms:
((12xy + 28x2) + -5y * (7x + 3y)) = 0
((12xy + 28x2) + -5y * (7x + 3y)) = 0
(12xy + 28x2 + (7x * -5y + 3y * -5y)) = 0
(12xy + 28x2 + (-35xy + -15y2)) = 0

Reorder the terms:
(12xy + -35xy + 28x2 + -15y2) = 0

Combine like terms: 12xy + -35xy = -23xy
(-23xy + 28x2 + -15y2) = 0

Solving
-23xy + 28x2 + -15y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -5y)(7x + 3y) = 0


Subproblem 1
Set the factor '(4x + -5y)' equal to zero and attempt to solve:

Simplifying
4x + -5y = 0

Solving
4x + -5y = 0

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

Add '5y' to each side of the equation.
4x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
4x + 0 = 0 + 5y
4x = 0 + 5y
Remove the zero:
4x = 5y

Divide each side by '4'.
x = 1.25y

Simplifying
x = 1.25y

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 = {1.25y, -0.4285714286y}

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