9y^2-48y+64-13(3y-8)+30=0

Solution for 9y^2-48y+64-13(3y-8)+30=0 equation:

Simplifying
9y2 + -48y + 64 + -13(3y + -8) + 30 = 0

Reorder the terms:
9y2 + -48y + 64 + -13(-8 + 3y) + 30 = 0
9y2 + -48y + 64 + (-8 * -13 + 3y * -13) + 30 = 0
9y2 + -48y + 64 + (104 + -39y) + 30 = 0

Reorder the terms:
64 + 104 + 30 + -48y + -39y + 9y2 = 0

Combine like terms: 64 + 104 = 168
168 + 30 + -48y + -39y + 9y2 = 0

Combine like terms: 168 + 30 = 198
198 + -48y + -39y + 9y2 = 0

Combine like terms: -48y + -39y = -87y
198 + -87y + 9y2 = 0

Solving
198 + -87y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(66 + -29y + 3y2) = 0

Factor a trinomial.
3((11 + -3y)(6 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(11 + -3y)' equal to zero and attempt to solve:

Simplifying
11 + -3y = 0

Solving
11 + -3y = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3y = 0 + -11
-3y = 0 + -11

Combine like terms: 0 + -11 = -11
-3y = -11

Divide each side by '-3'.
y = 3.666666667

Simplifying
y = 3.666666667
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {3.666666667, 6}