6(y^2-6y+9)-(y-3)-15=0

Solution for 6(y^2-6y+9)-(y-3)-15=0 equation:

Simplifying
6(y2 + -6y + 9) + -1(y + -3) + -15 = 0

Reorder the terms:
6(9 + -6y + y2) + -1(y + -3) + -15 = 0
(9 * 6 + -6y * 6 + y2 * 6) + -1(y + -3) + -15 = 0
(54 + -36y + 6y2) + -1(y + -3) + -15 = 0

Reorder the terms:
54 + -36y + 6y2 + -1(-3 + y) + -15 = 0
54 + -36y + 6y2 + (-3 * -1 + y * -1) + -15 = 0
54 + -36y + 6y2 + (3 + -1y) + -15 = 0

Reorder the terms:
54 + 3 + -15 + -36y + -1y + 6y2 = 0

Combine like terms: 54 + 3 = 57
57 + -15 + -36y + -1y + 6y2 = 0

Combine like terms: 57 + -15 = 42
42 + -36y + -1y + 6y2 = 0

Combine like terms: -36y + -1y = -37y
42 + -37y + 6y2 = 0

Solving
42 + -37y + 6y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + -2y)(14 + -3y) = 0

Subproblem 1
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 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 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Subproblem 2
Set the factor '(14 + -3y)' equal to zero and attempt to solve:

Simplifying
14 + -3y = 0

Solving
14 + -3y = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3y = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3y = 0 + -14
-3y = 0 + -14

Combine like terms: 0 + -14 = -14
-3y = -14

Divide each side by '-3'.
y = 4.666666667

Simplifying
y = 4.666666667
Solution
y = {1.5, 4.666666667}