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

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


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

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

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

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

Combine like terms: -4xy + 3xy = -1xy
(-1xy + x2 + -12y2) = 0

Solving
-1xy + x2 + -12y2 = 0

Solving for variable 'x'.

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


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

Simplifying
x + -4y = 0

Solving
x + -4y = 0

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

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

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

Simplifying
x = 4y

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 = {4y, -3y}

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