(2x+4y)(5x+8y)=

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Solution for (2x+4y)(5x+8y)= equation: 


Simplifying
(2x + 4y)(5x + 8y) = 0

Multiply (2x + 4y) * (5x + 8y)
(2x * (5x + 8y) + 4y * (5x + 8y)) = 0
((5x * 2x + 8y * 2x) + 4y * (5x + 8y)) = 0

Reorder the terms:
((16xy + 10x2) + 4y * (5x + 8y)) = 0
((16xy + 10x2) + 4y * (5x + 8y)) = 0
(16xy + 10x2 + (5x * 4y + 8y * 4y)) = 0
(16xy + 10x2 + (20xy + 32y2)) = 0

Reorder the terms:
(16xy + 20xy + 10x2 + 32y2) = 0

Combine like terms: 16xy + 20xy = 36xy
(36xy + 10x2 + 32y2) = 0

Solving
36xy + 10x2 + 32y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18xy + 5x2 + 16y2) = 0

Factor a trinomial.
2((5x + 8y)(x + 2y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5x + 8y)' equal to zero and attempt to solve:

Simplifying
5x + 8y = 0

Solving
5x + 8y = 0

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

Add '-8y' to each side of the equation.
5x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
5x + 0 = 0 + -8y
5x = 0 + -8y
Remove the zero:
5x = -8y

Divide each side by '5'.
x = -1.6y

Simplifying
x = -1.6y

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

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

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

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

Simplifying
x = -2y
Solution
x = {-1.6y, -2y}

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