y^2=9y^2+48y+64-64

Solution for y^2=9y^2+48y+64-64 equation:

Simplifying
y2 = 9y2 + 48y + 64 + -64

Reorder the terms:
y2 = 64 + -64 + 48y + 9y2

Combine like terms: 64 + -64 = 0
y2 = 0 + 48y + 9y2
y2 = 48y + 9y2

Solving
y2 = 48y + 9y2

Solving for variable 'y'.

Reorder the terms:
-48y + y2 + -9y2 = 48y + 9y2 + -48y + -9y2

Combine like terms: y2 + -9y2 = -8y2
-48y + -8y2 = 48y + 9y2 + -48y + -9y2

Reorder the terms:
-48y + -8y2 = 48y + -48y + 9y2 + -9y2

Combine like terms: 48y + -48y = 0
-48y + -8y2 = 0 + 9y2 + -9y2
-48y + -8y2 = 9y2 + -9y2

Combine like terms: 9y2 + -9y2 = 0
-48y + -8y2 = 0

Factor out the Greatest Common Factor (GCF), '-8y'.
-8y(6 + y) = 0

Ignore the factor -8.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 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 + y = 0 + -6

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

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

Simplifying
y = -6
Solution
y = {0, -6}