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

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


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

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

Reorder the terms:
((-15xy + 6x2) + 2y * (2x + -5y)) = 0
((-15xy + 6x2) + 2y * (2x + -5y)) = 0
(-15xy + 6x2 + (2x * 2y + -5y * 2y)) = 0
(-15xy + 6x2 + (4xy + -10y2)) = 0

Reorder the terms:
(-15xy + 4xy + 6x2 + -10y2) = 0

Combine like terms: -15xy + 4xy = -11xy
(-11xy + 6x2 + -10y2) = 0

Solving
-11xy + 6x2 + -10y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(2x + -5y)' equal to zero and attempt to solve:

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y

Subproblem 2
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
Solution
x = {2.5y, -0.6666666667y}

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