43y^2+12y+3=5

Solution for 43y^2+12y+3=5 equation:

Simplifying
43y2 + 12y + 3 = 5

Reorder the terms:
3 + 12y + 43y2 = 5

Solving
3 + 12y + 43y2 = 5

Solving for variable 'y'.

Reorder the terms:
3 + -5 + 12y + 43y2 = 5 + -5

Combine like terms: 3 + -5 = -2
-2 + 12y + 43y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-2 + 12y + 43y2 = 0

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

Divide each side by '43'.
-0.04651162791 + 0.2790697674y + y2 = 0

Move the constant term to the right:

Add '0.04651162791' to each side of the equation.
-0.04651162791 + 0.2790697674y + 0.04651162791 + y2 = 0 + 0.04651162791

Reorder the terms:
-0.04651162791 + 0.04651162791 + 0.2790697674y + y2 = 0 + 0.04651162791

Combine like terms: -0.04651162791 + 0.04651162791 = 0.00000000000
0.00000000000 + 0.2790697674y + y2 = 0 + 0.04651162791
0.2790697674y + y2 = 0 + 0.04651162791

Combine like terms: 0 + 0.04651162791 = 0.04651162791
0.2790697674y + y2 = 0.04651162791

The y term is 0.2790697674y.  Take half its coefficient (0.1395348837).
Square it (0.01946998377) and add it to both sides.

Add '0.01946998377' to each side of the equation.
0.2790697674y + 0.01946998377 + y2 = 0.04651162791 + 0.01946998377

Reorder the terms:
0.01946998377 + 0.2790697674y + y2 = 0.04651162791 + 0.01946998377

Combine like terms: 0.04651162791 + 0.01946998377 = 0.06598161168
0.01946998377 + 0.2790697674y + y2 = 0.06598161168

Factor a perfect square on the left side:
(y + 0.1395348837)(y + 0.1395348837) = 0.06598161168

Calculate the square root of the right side: 0.256868861

Break this problem into two subproblems by setting 
(y + 0.1395348837) equal to 0.256868861 and -0.256868861.

Subproblem 1
y + 0.1395348837 = 0.256868861

Simplifying
y + 0.1395348837 = 0.256868861

Reorder the terms:
0.1395348837 + y = 0.256868861

Solving
0.1395348837 + y = 0.256868861

Solving for variable 'y'.

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

Add '-0.1395348837' to each side of the equation.
0.1395348837 + -0.1395348837 + y = 0.256868861 + -0.1395348837

Combine like terms: 0.1395348837 + -0.1395348837 = 0.0000000000
0.0000000000 + y = 0.256868861 + -0.1395348837
y = 0.256868861 + -0.1395348837

Combine like terms: 0.256868861 + -0.1395348837 = 0.1173339773
y = 0.1173339773

Simplifying
y = 0.1173339773

Subproblem 2
y + 0.1395348837 = -0.256868861

Simplifying
y + 0.1395348837 = -0.256868861

Reorder the terms:
0.1395348837 + y = -0.256868861

Solving
0.1395348837 + y = -0.256868861

Solving for variable 'y'.

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

Add '-0.1395348837' to each side of the equation.
0.1395348837 + -0.1395348837 + y = -0.256868861 + -0.1395348837

Combine like terms: 0.1395348837 + -0.1395348837 = 0.0000000000
0.0000000000 + y = -0.256868861 + -0.1395348837
y = -0.256868861 + -0.1395348837

Combine like terms: -0.256868861 + -0.1395348837 = -0.3964037447
y = -0.3964037447

Simplifying
y = -0.3964037447

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.1173339773, -0.3964037447}