x^2+x(x-6)=0

Solution for x^2+x(x-6)=0 equation:

Simplifying
x2 + x(x + -6) = 0

Reorder the terms:
x2 + x(-6 + x) = 0
x2 + (-6 * x + x * x) = 0
x2 + (-6x + x2) = 0

Reorder the terms:
-6x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-6x + 2x2 = 0

Solving
-6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + x) = 0

Ignore the factor 2.
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 '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-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
Solution
x = {0, 3}