(x+4y)(2x+5y)=

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Solution for (x+4y)(2x+5y)= equation: 


Simplifying
(x + 4y)(2x + 5y) = 0

Multiply (x + 4y) * (2x + 5y)
(x(2x + 5y) + 4y * (2x + 5y)) = 0
((2x * x + 5y * x) + 4y * (2x + 5y)) = 0

Reorder the terms:
((5xy + 2x2) + 4y * (2x + 5y)) = 0
((5xy + 2x2) + 4y * (2x + 5y)) = 0
(5xy + 2x2 + (2x * 4y + 5y * 4y)) = 0
(5xy + 2x2 + (8xy + 20y2)) = 0

Reorder the terms:
(5xy + 8xy + 2x2 + 20y2) = 0

Combine like terms: 5xy + 8xy = 13xy
(13xy + 2x2 + 20y2) = 0

Solving
13xy + 2x2 + 20y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + 5y)(x + 4y) = 0


Subproblem 1
Set the factor '(2x + 5y)' equal to zero and attempt to solve:

Simplifying
2x + 5y = 0

Solving
2x + 5y = 0

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

Add '-5y' to each side of the equation.
2x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
2x + 0 = 0 + -5y
2x = 0 + -5y
Remove the zero:
2x = -5y

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y

Subproblem 2
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
Solution
x = {-2.5y, -4y}

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