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

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


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

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

Reorder the terms:
((9xy + 3x2) + 4y * (x + 3y)) = 0
((9xy + 3x2) + 4y * (x + 3y)) = 0
(9xy + 3x2 + (x * 4y + 3y * 4y)) = 0
(9xy + 3x2 + (4xy + 12y2)) = 0

Reorder the terms:
(9xy + 4xy + 3x2 + 12y2) = 0

Combine like terms: 9xy + 4xy = 13xy
(13xy + 3x2 + 12y2) = 0

Solving
13xy + 3x2 + 12y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(3x + 4y)' equal to zero and attempt to solve:

Simplifying
3x + 4y = 0

Solving
3x + 4y = 0

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

Add '-4y' to each side of the equation.
3x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
3x + 0 = 0 + -4y
3x = 0 + -4y
Remove the zero:
3x = -4y

Divide each side by '3'.
x = -1.333333333y

Simplifying
x = -1.333333333y

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 = {-1.333333333y, -3y}

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