(2x+3y)*(4x+5y)=0

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Solution for (2x+3y)*(4x+5y)=0 equation: 


Simplifying
(2x + 3y)(4x + 5y) = 0

Multiply (2x + 3y) * (4x + 5y)
(2x * (4x + 5y) + 3y * (4x + 5y)) = 0
((4x * 2x + 5y * 2x) + 3y * (4x + 5y)) = 0

Reorder the terms:
((10xy + 8x2) + 3y * (4x + 5y)) = 0
((10xy + 8x2) + 3y * (4x + 5y)) = 0
(10xy + 8x2 + (4x * 3y + 5y * 3y)) = 0
(10xy + 8x2 + (12xy + 15y2)) = 0

Reorder the terms:
(10xy + 12xy + 8x2 + 15y2) = 0

Combine like terms: 10xy + 12xy = 22xy
(22xy + 8x2 + 15y2) = 0

Solving
22xy + 8x2 + 15y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + 5y)(2x + 3y) = 0


Subproblem 1
Set the factor '(4x + 5y)' equal to zero and attempt to solve:

Simplifying
4x + 5y = 0

Solving
4x + 5y = 0

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

Add '-5y' to each side of the equation.
4x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
4x + 0 = 0 + -5y
4x = 0 + -5y
Remove the zero:
4x = -5y

Divide each side by '4'.
x = -1.25y

Simplifying
x = -1.25y

Subproblem 2
Set the factor '(2x + 3y)' equal to zero and attempt to solve:

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y
Solution
x = {-1.25y, -1.5y}

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