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

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


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

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

Reorder the terms:
((-5xy + 3x2) + 7y * (3x + -5y)) = 0
((-5xy + 3x2) + 7y * (3x + -5y)) = 0
(-5xy + 3x2 + (3x * 7y + -5y * 7y)) = 0
(-5xy + 3x2 + (21xy + -35y2)) = 0

Reorder the terms:
(-5xy + 21xy + 3x2 + -35y2) = 0

Combine like terms: -5xy + 21xy = 16xy
(16xy + 3x2 + -35y2) = 0

Solving
16xy + 3x2 + -35y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
x + 7y = 0

Solving
x + 7y = 0

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

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

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

Simplifying
x = -7y
Solution
x = {1.666666667y, -7y}

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