(4x+6y)(x+3y)=

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Solution for (4x+6y)(x+3y)= equation: 


Simplifying
(4x + 6y)(x + 3y) = 0

Multiply (4x + 6y) * (x + 3y)
(4x * (x + 3y) + 6y * (x + 3y)) = 0
((x * 4x + 3y * 4x) + 6y * (x + 3y)) = 0

Reorder the terms:
((12xy + 4x2) + 6y * (x + 3y)) = 0
((12xy + 4x2) + 6y * (x + 3y)) = 0
(12xy + 4x2 + (x * 6y + 3y * 6y)) = 0
(12xy + 4x2 + (6xy + 18y2)) = 0

Reorder the terms:
(12xy + 6xy + 4x2 + 18y2) = 0

Combine like terms: 12xy + 6xy = 18xy
(18xy + 4x2 + 18y2) = 0

Solving
18xy + 4x2 + 18y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9xy + 2x2 + 9y2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(2x + 3y)' equal to zero and attempt to solve:

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y

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 = {-1.5y, -3y}

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