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

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


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

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

Reorder the terms:
((-5xy + 3x2) + 4y * (3x + -5y)) = 0
((-5xy + 3x2) + 4y * (3x + -5y)) = 0
(-5xy + 3x2 + (3x * 4y + -5y * 4y)) = 0
(-5xy + 3x2 + (12xy + -20y2)) = 0

Reorder the terms:
(-5xy + 12xy + 3x2 + -20y2) = 0

Combine like terms: -5xy + 12xy = 7xy
(7xy + 3x2 + -20y2) = 0

Solving
7xy + 3x2 + -20y2 = 0

Solving for variable 'x'.

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

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

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

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

Simplifying
x = -4y
Solution
x = {1.666666667y, -4y}

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