y^2-6y+9y=0

Solution for y^2-6y+9y=0 equation:

Simplifying
y2 + -6y + 9y = 0

Reorder the terms:
-6y + 9y + y2 = 0

Combine like terms: -6y + 9y = 3y
3y + y2 = 0

Solving
3y + y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + y) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

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

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

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

Simplifying
y = -3
Solution
y = {0, -3}