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

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


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

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

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

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

Combine like terms: 4xy + 2xy = 6xy
(6xy + 4x2 + 2y2) = 0

Solving
6xy + 4x2 + 2y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3xy + 2x2 + y2) = 0

Factor a trinomial.
2((2x + y)(x + y)) = 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 + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {-0.5y, -1y}

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