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

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

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

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

Reorder the terms:
((16xy + 4x2) + y(2x + 8y)) = 0
((16xy + 4x2) + y(2x + 8y)) = 0
(16xy + 4x2 + (2x * y + 8y * y)) = 0
(16xy + 4x2 + (2xy + 8y2)) = 0

Reorder the terms:
(16xy + 2xy + 4x2 + 8y2) = 0

Combine like terms: 16xy + 2xy = 18xy
(18xy + 4x2 + 8y2) = 0

Solving
18xy + 4x2 + 8y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9xy + 2x2 + 4y2) = 0

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

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
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 = {-0.5y, -4y}