x^2y+4xy-21y=

Solution for x^2y+4xy-21y= equation:

Simplifying
x2y + 4xy + -21y = 0

Reorder the terms:
4xy + x2y + -21y = 0

Solving
4xy + x2y + -21y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(4x + x2 + -21) = 0

Factor a trinomial.
y((x + -3)(x + 7)) = 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 '(x + -3)' equal to zero and attempt to solve:

Simplifying
x + -3 = 0

Reorder the terms:
-3 + x = 0

Solving
-3 + x = 0

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

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

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Subproblem 3
Set the factor '(x + 7)' equal to zero and attempt to solve:

Simplifying
x + 7 = 0

Reorder the terms:
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {3, -7}