(x+7y)(3x+4y)=0

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Solution for (x+7y)(3x+4y)=0 equation: 


Simplifying
(x + 7y)(3x + 4y) = 0

Multiply (x + 7y) * (3x + 4y)
(x(3x + 4y) + 7y * (3x + 4y)) = 0
((3x * x + 4y * x) + 7y * (3x + 4y)) = 0

Reorder the terms:
((4xy + 3x2) + 7y * (3x + 4y)) = 0
((4xy + 3x2) + 7y * (3x + 4y)) = 0
(4xy + 3x2 + (3x * 7y + 4y * 7y)) = 0
(4xy + 3x2 + (21xy + 28y2)) = 0

Reorder the terms:
(4xy + 21xy + 3x2 + 28y2) = 0

Combine like terms: 4xy + 21xy = 25xy
(25xy + 3x2 + 28y2) = 0

Solving
25xy + 3x2 + 28y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + 4y)(x + 7y) = 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 '(x + 7y)' equal to zero and attempt to solve:

Simplifying
x + 7y = 0

Solving
x + 7y = 0

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

Add '-7y' to each side of the equation.
x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
x + 0 = 0 + -7y
x = 0 + -7y
Remove the zero:
x = -7y

Simplifying
x = -7y
Solution
x = {-1.333333333y, -7y}

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