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

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


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

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

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

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

Combine like terms: 3xy + -16xy = -13xy
(-13xy + 12x2 + -4y2) = 0

Solving
-13xy + 12x2 + -4y2 = 0

Solving for variable 'x'.

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

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