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

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


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

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

Reorder the terms:
((9xy + 12x2) + 5y * (4x + 3y)) = 0
((9xy + 12x2) + 5y * (4x + 3y)) = 0
(9xy + 12x2 + (4x * 5y + 3y * 5y)) = 0
(9xy + 12x2 + (20xy + 15y2)) = 0

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

Combine like terms: 9xy + 20xy = 29xy
(29xy + 12x2 + 15y2) = 0

Solving
29xy + 12x2 + 15y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + 3y)(3x + 5y) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.75y, -1.666666667y}

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