(15y^2)-42y+27=0

Solution for (15y^2)-42y+27=0 equation:

Simplifying
(15y2) + -42y + 27 = 0

Reorder the terms:
27 + -42y + (15y2) = 0

Solving
27 + -42y + (15y2) = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -14y + (5y2)) = 0

Factor a trinomial.
3((1 + -1y)(9 + -5y)) = 0

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Subproblem 2
Set the factor '(9 + -5y)' equal to zero and attempt to solve:

Simplifying
9 + -5y = 0

Solving
9 + -5y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5y = 0 + -9
-5y = 0 + -9

Combine like terms: 0 + -9 = -9
-5y = -9

Divide each side by '-5'.
y = 1.8

Simplifying
y = 1.8
Solution
y = {1, 1.8}