(4y-12)+(22y^2+14y-16)=

Solution for (4y-12)+(22y^2+14y-16)= equation:

Simplifying
(4y + -12) + (22y2 + 14y + -16) = 0

Reorder the terms:
(-12 + 4y) + (22y2 + 14y + -16) = 0

Remove parenthesis around (-12 + 4y)
-12 + 4y + (22y2 + 14y + -16) = 0

Reorder the terms:
-12 + 4y + (-16 + 14y + 22y2) = 0

Remove parenthesis around (-16 + 14y + 22y2)
-12 + 4y + -16 + 14y + 22y2 = 0

Reorder the terms:
-12 + -16 + 4y + 14y + 22y2 = 0

Combine like terms: -12 + -16 = -28
-28 + 4y + 14y + 22y2 = 0

Combine like terms: 4y + 14y = 18y
-28 + 18y + 22y2 = 0

Solving
-28 + 18y + 22y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 9y + 11y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + 9y + 11y2)' equal to zero and attempt to solve:

Simplifying
-14 + 9y + 11y2 = 0

Solving
-14 + 9y + 11y2 = 0

Begin completing the square.  Divide all terms by
11 the coefficient of the squared term: 

Divide each side by '11'.
-1.272727273 + 0.8181818182y + y2 = 0

Move the constant term to the right:

Add '1.272727273' to each side of the equation.
-1.272727273 + 0.8181818182y + 1.272727273 + y2 = 0 + 1.272727273

Reorder the terms:
-1.272727273 + 1.272727273 + 0.8181818182y + y2 = 0 + 1.272727273

Combine like terms: -1.272727273 + 1.272727273 = 0.000000000
0.000000000 + 0.8181818182y + y2 = 0 + 1.272727273
0.8181818182y + y2 = 0 + 1.272727273

Combine like terms: 0 + 1.272727273 = 1.272727273
0.8181818182y + y2 = 1.272727273

The y term is 0.8181818182y.  Take half its coefficient (0.4090909091).
Square it (0.1673553719) and add it to both sides.

Add '0.1673553719' to each side of the equation.
0.8181818182y + 0.1673553719 + y2 = 1.272727273 + 0.1673553719

Reorder the terms:
0.1673553719 + 0.8181818182y + y2 = 1.272727273 + 0.1673553719

Combine like terms: 1.272727273 + 0.1673553719 = 1.4400826449
0.1673553719 + 0.8181818182y + y2 = 1.4400826449

Factor a perfect square on the left side:
(y + 0.4090909091)(y + 0.4090909091) = 1.4400826449

Calculate the square root of the right side: 1.200034435

Break this problem into two subproblems by setting 
(y + 0.4090909091) equal to 1.200034435 and -1.200034435.

Subproblem 1
y + 0.4090909091 = 1.200034435

Simplifying
y + 0.4090909091 = 1.200034435

Reorder the terms:
0.4090909091 + y = 1.200034435

Solving
0.4090909091 + y = 1.200034435

Solving for variable 'y'.

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

Add '-0.4090909091' to each side of the equation.
0.4090909091 + -0.4090909091 + y = 1.200034435 + -0.4090909091

Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000
0.0000000000 + y = 1.200034435 + -0.4090909091
y = 1.200034435 + -0.4090909091

Combine like terms: 1.200034435 + -0.4090909091 = 0.7909435259
y = 0.7909435259

Simplifying
y = 0.7909435259

Subproblem 2
y + 0.4090909091 = -1.200034435

Simplifying
y + 0.4090909091 = -1.200034435

Reorder the terms:
0.4090909091 + y = -1.200034435

Solving
0.4090909091 + y = -1.200034435

Solving for variable 'y'.

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

Add '-0.4090909091' to each side of the equation.
0.4090909091 + -0.4090909091 + y = -1.200034435 + -0.4090909091

Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000
0.0000000000 + y = -1.200034435 + -0.4090909091
y = -1.200034435 + -0.4090909091

Combine like terms: -1.200034435 + -0.4090909091 = -1.6091253441
y = -1.6091253441

Simplifying
y = -1.6091253441

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.7909435259, -1.6091253441}
Solution
y = {0.7909435259, -1.6091253441}