(7x-2y)(5x-3y)=

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Solution for (7x-2y)(5x-3y)= equation: 


Simplifying
(7x + -2y)(5x + -3y) = 0

Multiply (7x + -2y) * (5x + -3y)
(7x * (5x + -3y) + -2y * (5x + -3y)) = 0
((5x * 7x + -3y * 7x) + -2y * (5x + -3y)) = 0

Reorder the terms:
((-21xy + 35x2) + -2y * (5x + -3y)) = 0
((-21xy + 35x2) + -2y * (5x + -3y)) = 0
(-21xy + 35x2 + (5x * -2y + -3y * -2y)) = 0
(-21xy + 35x2 + (-10xy + 6y2)) = 0

Reorder the terms:
(-21xy + -10xy + 35x2 + 6y2) = 0

Combine like terms: -21xy + -10xy = -31xy
(-31xy + 35x2 + 6y2) = 0

Solving
-31xy + 35x2 + 6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -3y)(7x + -2y) = 0


Subproblem 1
Set the factor '(5x + -3y)' equal to zero and attempt to solve:

Simplifying
5x + -3y = 0

Solving
5x + -3y = 0

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

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

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

Divide each side by '5'.
x = 0.6y

Simplifying
x = 0.6y

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

Simplifying
7x + -2y = 0

Solving
7x + -2y = 0

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

Add '2y' to each side of the equation.
7x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
7x + 0 = 0 + 2y
7x = 0 + 2y
Remove the zero:
7x = 2y

Divide each side by '7'.
x = 0.2857142857y

Simplifying
x = 0.2857142857y
Solution
x = {0.6y, 0.2857142857y}

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