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

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


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

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

Reorder the terms:
((4xy + 5x2) + 3y * (5x + 4y)) = 0
((4xy + 5x2) + 3y * (5x + 4y)) = 0
(4xy + 5x2 + (5x * 3y + 4y * 3y)) = 0
(4xy + 5x2 + (15xy + 12y2)) = 0

Reorder the terms:
(4xy + 15xy + 5x2 + 12y2) = 0

Combine like terms: 4xy + 15xy = 19xy
(19xy + 5x2 + 12y2) = 0

Solving
19xy + 5x2 + 12y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + 4y)(x + 3y) = 0


Subproblem 1
Set the factor '(5x + 4y)' equal to zero and attempt to solve:

Simplifying
5x + 4y = 0

Solving
5x + 4y = 0

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

Add '-4y' to each side of the equation.
5x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
5x + 0 = 0 + -4y
5x = 0 + -4y
Remove the zero:
5x = -4y

Divide each side by '5'.
x = -0.8y

Simplifying
x = -0.8y

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 = {-0.8y, -3y}

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