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

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

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

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

Reorder the terms:
((2xy + x2) + 3y * (x + 2y)) = 0
((2xy + x2) + 3y * (x + 2y)) = 0
(2xy + x2 + (x * 3y + 2y * 3y)) = 0
(2xy + x2 + (3xy + 6y2)) = 0

Reorder the terms:
(2xy + 3xy + x2 + 6y2) = 0

Combine like terms: 2xy + 3xy = 5xy
(5xy + x2 + 6y2) = 0

Solving
5xy + x2 + 6y2 = 0

Solving for variable 'x'.

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

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

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

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

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

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

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

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

Simplifying
x = -3y
Solution
x = {-2y, -3y}