(3x+2y)(4x+y)=

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Solution for (3x+2y)(4x+y)= equation: 


Simplifying
(3x + 2y)(4x + y) = 0

Multiply (3x + 2y) * (4x + y)
(3x * (4x + y) + 2y * (4x + y)) = 0
((4x * 3x + y * 3x) + 2y * (4x + y)) = 0

Reorder the terms:
((3xy + 12x2) + 2y * (4x + y)) = 0
((3xy + 12x2) + 2y * (4x + y)) = 0
(3xy + 12x2 + (4x * 2y + y * 2y)) = 0
(3xy + 12x2 + (8xy + 2y2)) = 0

Reorder the terms:
(3xy + 8xy + 12x2 + 2y2) = 0

Combine like terms: 3xy + 8xy = 11xy
(11xy + 12x2 + 2y2) = 0

Solving
11xy + 12x2 + 2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + y)(3x + 2y) = 0


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

Simplifying
4x + y = 0

Solving
4x + y = 0

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

Add '-1y' to each side of the equation.
4x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
4x + 0 = 0 + -1y
4x = 0 + -1y
Remove the zero:
4x = -1y

Divide each side by '4'.
x = -0.25y

Simplifying
x = -0.25y

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

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

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

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

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y
Solution
x = {-0.25y, -0.6666666667y}

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