30x^4y+105x^3y^2+45x^2y^3=

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Solution for 30x^4y+105x^3y^2+45x^2y^3= equation: 


Simplifying
30x4y + 105x3y2 + 45x2y3 = 0

Reorder the terms:
45x2y3 + 105x3y2 + 30x4y = 0

Solving
45x2y3 + 105x3y2 + 30x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15x2y'.
15x2y(3y2 + 7xy + 2x2) = 0

Factor a trinomial.
15x2y((3y + x)(y + 2x)) = 0

Ignore the factor 15.

Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 0

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

Simplifying
3y + x = 0

Reorder the terms:
x + 3y = 0

Solving
x + 3y = 0

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

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

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

Simplifying
x = -3y

Subproblem 3
Set the factor '(y + 2x)' equal to zero and attempt to solve:

Simplifying
y + 2x = 0

Reorder the terms:
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
Solution
x = {-3y, -0.5y}

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