3y^2-48y+48=0

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Solution for 3y^2-48y+48=0 equation: 


Simplifying
3y2 + -48y + 48 = 0

Reorder the terms:
48 + -48y + 3y2 = 0

Solving
48 + -48y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + -16y + y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(16 + -16y + y2)' equal to zero and attempt to solve:

Simplifying
16 + -16y + y2 = 0

Solving
16 + -16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -16y + -16 + y2 = 0 + -16

Reorder the terms:
16 + -16 + -16y + y2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -16y + y2 = 0 + -16
-16y + y2 = 0 + -16

Combine like terms: 0 + -16 = -16
-16y + y2 = -16

The y term is -16y.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16y + 64 + y2 = -16 + 64

Reorder the terms:
64 + -16y + y2 = -16 + 64

Combine like terms: -16 + 64 = 48
64 + -16y + y2 = 48

Factor a perfect square on the left side:
(y + -8)(y + -8) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(y + -8) equal to 6.92820323 and -6.92820323.


Subproblem 1
y + -8 = 6.92820323

Simplifying
y + -8 = 6.92820323

Reorder the terms:
-8 + y = 6.92820323

Solving
-8 + y = 6.92820323

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = 6.92820323 + 8

Combine like terms: -8 + 8 = 0
0 + y = 6.92820323 + 8
y = 6.92820323 + 8

Combine like terms: 6.92820323 + 8 = 14.92820323
y = 14.92820323

Simplifying
y = 14.92820323


Subproblem 2
y + -8 = -6.92820323

Simplifying
y + -8 = -6.92820323

Reorder the terms:
-8 + y = -6.92820323

Solving
-8 + y = -6.92820323

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = -6.92820323 + 8

Combine like terms: -8 + 8 = 0
0 + y = -6.92820323 + 8
y = -6.92820323 + 8

Combine like terms: -6.92820323 + 8 = 1.07179677
y = 1.07179677

Simplifying
y = 1.07179677


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.92820323, 1.07179677}
Solution
y = {14.92820323, 1.07179677}

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