(xy+y^2)(4x+3y)=

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Solution for (xy+y^2)(4x+3y)= equation: 


Simplifying
(xy + y2)(4x + 3y) = 0

Multiply (xy + y2) * (4x + 3y)
(xy(4x + 3y) + y2(4x + 3y)) = 0
((4x * xy + 3y * xy) + y2(4x + 3y)) = 0

Reorder the terms:
((3xy2 + 4x2y) + y2(4x + 3y)) = 0
((3xy2 + 4x2y) + y2(4x + 3y)) = 0
(3xy2 + 4x2y + (4x * y2 + 3y * y2)) = 0
(3xy2 + 4x2y + (4xy2 + 3y3)) = 0

Reorder the terms:
(3xy2 + 4xy2 + 4x2y + 3y3) = 0

Combine like terms: 3xy2 + 4xy2 = 7xy2
(7xy2 + 4x2y + 3y3) = 0

Solving
7xy2 + 4x2y + 3y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(7xy + 4x2 + 3y2) = 0

Factor a trinomial.
y((4x + 3y)(x + y)) = 0


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 '(4x + 3y)' equal to zero and attempt to solve:

Simplifying
4x + 3y = 0

Solving
4x + 3y = 0

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

Add '-3y' to each side of the equation.
4x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
4x + 0 = 0 + -3y
4x = 0 + -3y
Remove the zero:
4x = -3y

Divide each side by '4'.
x = -0.75y

Simplifying
x = -0.75y

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 = {-0.75y, -1y}

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