30y^2-69y+18=0

Solution for 30y^2-69y+18=0 equation:

Simplifying
30y2 + -69y + 18 = 0

Reorder the terms:
18 + -69y + 30y2 = 0

Solving
18 + -69y + 30y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -23y + 10y2) = 0

Factor a trinomial.
3((3 + -10y)(2 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -10y)' equal to zero and attempt to solve:

Simplifying
3 + -10y = 0

Solving
3 + -10y = 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 + -10y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -10y = 0 + -3
-10y = 0 + -3

Combine like terms: 0 + -3 = -3
-10y = -3

Divide each side by '-10'.
y = 0.3

Simplifying
y = 0.3
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {0.3, 2}