(4x+4y)(x+3y)=

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Solution for (4x+4y)(x+3y)= equation: 


Simplifying
(4x + 4y)(x + 3y) = 0

Multiply (4x + 4y) * (x + 3y)
(4x * (x + 3y) + 4y * (x + 3y)) = 0
((x * 4x + 3y * 4x) + 4y * (x + 3y)) = 0

Reorder the terms:
((12xy + 4x2) + 4y * (x + 3y)) = 0
((12xy + 4x2) + 4y * (x + 3y)) = 0
(12xy + 4x2 + (x * 4y + 3y * 4y)) = 0
(12xy + 4x2 + (4xy + 12y2)) = 0

Reorder the terms:
(12xy + 4xy + 4x2 + 12y2) = 0

Combine like terms: 12xy + 4xy = 16xy
(16xy + 4x2 + 12y2) = 0

Solving
16xy + 4x2 + 12y2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 4.

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}

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