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

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


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

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

Reorder the terms:
((-20xy + 12x2) + 3y * (3x + -5y)) = 0
((-20xy + 12x2) + 3y * (3x + -5y)) = 0
(-20xy + 12x2 + (3x * 3y + -5y * 3y)) = 0
(-20xy + 12x2 + (9xy + -15y2)) = 0

Reorder the terms:
(-20xy + 9xy + 12x2 + -15y2) = 0

Combine like terms: -20xy + 9xy = -11xy
(-11xy + 12x2 + -15y2) = 0

Solving
-11xy + 12x2 + -15y2 = 0

Solving for variable 'x'.

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

Simplifying
4x + 3y = 0

Solving
4x + 3y = 0

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

Add '-3y' to each side of the equation.
4x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
4x + 0 = 0 + -3y
4x = 0 + -3y
Remove the zero:
4x = -3y

Divide each side by '4'.
x = -0.75y

Simplifying
x = -0.75y
Solution
x = {1.666666667y, -0.75y}

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