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

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

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

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

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

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

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

Solving
0 = -5xy + 2x2 + -3y2

Solving for variable 'x'.
Remove the zero:
5xy + -2x2 + 3y2 = -5xy + 2x2 + -3y2 + 5xy + -2x2 + 3y2

Reorder the terms:
5xy + -2x2 + 3y2 = -5xy + 5xy + 2x2 + -2x2 + -3y2 + 3y2

Combine like terms: -5xy + 5xy = 0
5xy + -2x2 + 3y2 = 0 + 2x2 + -2x2 + -3y2 + 3y2
5xy + -2x2 + 3y2 = 2x2 + -2x2 + -3y2 + 3y2

Combine like terms: 2x2 + -2x2 = 0
5xy + -2x2 + 3y2 = 0 + -3y2 + 3y2
5xy + -2x2 + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
5xy + -2x2 + 3y2 = 0

Factor a trinomial.
(-2x + -1y)(x + -3y) = 0

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

Simplifying
-2x + -1y = 0

Solving
-2x + -1y = 0

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

Add 'y' to each side of the equation.
-2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-2x + 0 = 0 + y
-2x = 0 + y
Remove the zero:
-2x = y

Divide each side by '-2'.
x = -0.5y

Simplifying
x = -0.5y
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 = {-0.5y, 3y}