4y^2-44y+12=

Solution for 4y^2-44y+12= equation:

Simplifying
4y2 + -44y + 12 = 0

Reorder the terms:
12 + -44y + 4y2 = 0

Solving
12 + -44y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -11y + y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -11y + y2)' equal to zero and attempt to solve:

Simplifying
3 + -11y + y2 = 0

Solving
3 + -11y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -11y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + -11y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -11y + y2 = 0 + -3
-11y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-11y + y2 = -3

The y term is -11y.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11y + 30.25 + y2 = -3 + 30.25

Reorder the terms:
30.25 + -11y + y2 = -3 + 30.25

Combine like terms: -3 + 30.25 = 27.25
30.25 + -11y + y2 = 27.25

Factor a perfect square on the left side:
(y + -5.5)(y + -5.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(y + -5.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
y + -5.5 = 5.220153254

Simplifying
y + -5.5 = 5.220153254

Reorder the terms:
-5.5 + y = 5.220153254

Solving
-5.5 + y = 5.220153254

Solving for variable 'y'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + y = 5.220153254 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = 5.220153254 + 5.5
y = 5.220153254 + 5.5

Combine like terms: 5.220153254 + 5.5 = 10.720153254
y = 10.720153254

Simplifying
y = 10.720153254

Subproblem 2
y + -5.5 = -5.220153254

Simplifying
y + -5.5 = -5.220153254

Reorder the terms:
-5.5 + y = -5.220153254

Solving
-5.5 + y = -5.220153254

Solving for variable 'y'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + y = -5.220153254 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = -5.220153254 + 5.5
y = -5.220153254 + 5.5

Combine like terms: -5.220153254 + 5.5 = 0.279846746
y = 0.279846746

Simplifying
y = 0.279846746

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.720153254, 0.279846746}
Solution
y = {10.720153254, 0.279846746}