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

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


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

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

Reorder the terms:
((16xy + 12x2) + y(3x + 4y)) = 0
((16xy + 12x2) + y(3x + 4y)) = 0
(16xy + 12x2 + (3x * y + 4y * y)) = 0
(16xy + 12x2 + (3xy + 4y2)) = 0

Reorder the terms:
(16xy + 3xy + 12x2 + 4y2) = 0

Combine like terms: 16xy + 3xy = 19xy
(19xy + 12x2 + 4y2) = 0

Solving
19xy + 12x2 + 4y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + y)(3x + 4y) = 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 + 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
Solution
x = {-0.25y, -1.333333333y}

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