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

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


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

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

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

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

Combine like terms: 2xy + 2xy = 4xy
y(4xy + 2x2 + 2y2) = 0
(4xy * y + 2x2 * y + 2y2 * y) = 0
(4xy2 + 2x2y + 2y3) = 0

Solving
4xy2 + 2x2y + 2y3 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

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

Subproblem 3

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 = {-1y, -1y}

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