x^2+7xy=0

Solution for x^2+7xy=0 equation:

Simplifying
x2 + 7xy = 0

Reorder the terms:
7xy + x2 = 0

Solving
7xy + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7y + x) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(7y + x)' equal to zero and attempt to solve:

Simplifying
7y + x = 0

Reorder the terms:
x + 7y = 0

Solving
x + 7y = 0

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

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

Combine like terms: 7y + -7y = 0
x + 0 = 0 + -7y
x = 0 + -7y
Remove the zero:
x = -7y

Simplifying
x = -7y
Solution
x = {0, -7y}