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

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


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

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

Reorder the terms:
((-10xy + 15x2) + 7y * (3x + -2y)) = 0
((-10xy + 15x2) + 7y * (3x + -2y)) = 0
(-10xy + 15x2 + (3x * 7y + -2y * 7y)) = 0
(-10xy + 15x2 + (21xy + -14y2)) = 0

Reorder the terms:
(-10xy + 21xy + 15x2 + -14y2) = 0

Combine like terms: -10xy + 21xy = 11xy
(11xy + 15x2 + -14y2) = 0

Solving
11xy + 15x2 + -14y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(5x + 7y)' equal to zero and attempt to solve:

Simplifying
5x + 7y = 0

Solving
5x + 7y = 0

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

Add '-7y' to each side of the equation.
5x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
5x + 0 = 0 + -7y
5x = 0 + -7y
Remove the zero:
5x = -7y

Divide each side by '5'.
x = -1.4y

Simplifying
x = -1.4y
Solution
x = {0.6666666667y, -1.4y}

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