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

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

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

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

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

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

Combine like terms: -3xy + xy = -2xy
2(-2xy + x2 + -3y2) = 0
(-2xy * 2 + x2 * 2 + -3y2 * 2) = 0
(-4xy + 2x2 + -6y2) = 0

Solving
-4xy + 2x2 + -6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2xy + x2 + -3y2) = 0

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

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {3y, -1y}