(x+5y)(3x+4y)=

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Solution for (x+5y)(3x+4y)= equation: 


Simplifying
(x + 5y)(3x + 4y) = 0

Multiply (x + 5y) * (3x + 4y)
(x(3x + 4y) + 5y * (3x + 4y)) = 0
((3x * x + 4y * x) + 5y * (3x + 4y)) = 0

Reorder the terms:
((4xy + 3x2) + 5y * (3x + 4y)) = 0
((4xy + 3x2) + 5y * (3x + 4y)) = 0
(4xy + 3x2 + (3x * 5y + 4y * 5y)) = 0
(4xy + 3x2 + (15xy + 20y2)) = 0

Reorder the terms:
(4xy + 15xy + 3x2 + 20y2) = 0

Combine like terms: 4xy + 15xy = 19xy
(19xy + 3x2 + 20y2) = 0

Solving
19xy + 3x2 + 20y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + 4y)(x + 5y) = 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 + 5y)' equal to zero and attempt to solve:

Simplifying
x + 5y = 0

Solving
x + 5y = 0

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

Add '-5y' to each side of the equation.
x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
x + 0 = 0 + -5y
x = 0 + -5y
Remove the zero:
x = -5y

Simplifying
x = -5y
Solution
x = {-1.333333333y, -5y}

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