10x^2y+10xy-420y=0

Solution for 10x^2y+10xy-420y=0 equation:

Simplifying
10x2y + 10xy + -420y = 0

Reorder the terms:
10xy + 10x2y + -420y = 0

Solving
10xy + 10x2y + -420y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10y'.
10y(x + x2 + -42) = 0

Factor a trinomial.
10y((x + -6)(x + 7)) = 0

Ignore the factor 10.
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 + -6)' equal to zero and attempt to solve:

Simplifying
x + -6 = 0

Reorder the terms:
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, -7}