15y^2-27y+2=y+6

Solution for 15y^2-27y+2=y+6 equation:

Simplifying
15y2 + -27y + 2 = y + 6

Reorder the terms:
2 + -27y + 15y2 = y + 6

Reorder the terms:
2 + -27y + 15y2 = 6 + y

Solving
2 + -27y + 15y2 = 6 + y

Solving for variable 'y'.

Reorder the terms:
2 + -6 + -27y + -1y + 15y2 = 6 + y + -6 + -1y

Combine like terms: 2 + -6 = -4
-4 + -27y + -1y + 15y2 = 6 + y + -6 + -1y

Combine like terms: -27y + -1y = -28y
-4 + -28y + 15y2 = 6 + y + -6 + -1y

Reorder the terms:
-4 + -28y + 15y2 = 6 + -6 + y + -1y

Combine like terms: 6 + -6 = 0
-4 + -28y + 15y2 = 0 + y + -1y
-4 + -28y + 15y2 = y + -1y

Combine like terms: y + -1y = 0
-4 + -28y + 15y2 = 0

Factor a trinomial.
(-2 + -15y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-2 + -15y)' equal to zero and attempt to solve:

Simplifying
-2 + -15y = 0

Solving
-2 + -15y = 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 + -15y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -15y = 0 + 2
-15y = 0 + 2

Combine like terms: 0 + 2 = 2
-15y = 2

Divide each side by '-15'.
y = -0.1333333333

Simplifying
y = -0.1333333333
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 = {-0.1333333333, 2}