(3x-2y)(4x+5y)=

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


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

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

Reorder the terms:
((15xy + 12x2) + -2y * (4x + 5y)) = 0
((15xy + 12x2) + -2y * (4x + 5y)) = 0
(15xy + 12x2 + (4x * -2y + 5y * -2y)) = 0
(15xy + 12x2 + (-8xy + -10y2)) = 0

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

Combine like terms: 15xy + -8xy = 7xy
(7xy + 12x2 + -10y2) = 0

Solving
7xy + 12x2 + -10y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve:

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

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

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

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y

Subproblem 2
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
Solution
x = {0.6666666667y, -1.25y}

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