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

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

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

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

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

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

Combine like terms: 3xy + xy = 4xy
3(4xy + x2 + 3y2) = 0
(4xy * 3 + x2 * 3 + 3y2 * 3) = 0
(12xy + 3x2 + 9y2) = 0

Solving
12xy + 3x2 + 9y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4xy + x2 + 3y2) = 0

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

Ignore the factor 3.
Subproblem 1
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
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 = {-1y, -3y}