3y^2+14y-12=0

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Solution for 3y^2+14y-12=0 equation: 


Simplifying
3y2 + 14y + -12 = 0

Reorder the terms:
-12 + 14y + 3y2 = 0

Solving
-12 + 14y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-4 + 4.666666667y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 4.666666667y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + 4.666666667y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4.666666667y + y2 = 0 + 4
4.666666667y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
4.666666667y + y2 = 4

The y term is 4.666666667y.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667y + 5.444444448 + y2 = 4 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667y + y2 = 4 + 5.444444448

Combine like terms: 4 + 5.444444448 = 9.444444448
5.444444448 + 4.666666667y + y2 = 9.444444448

Factor a perfect square on the left side:
(y + 2.333333334)(y + 2.333333334) = 9.444444448

Calculate the square root of the right side: 3.073181486

Break this problem into two subproblems by setting 
(y + 2.333333334) equal to 3.073181486 and -3.073181486.


Subproblem 1
y + 2.333333334 = 3.073181486

Simplifying
y + 2.333333334 = 3.073181486

Reorder the terms:
2.333333334 + y = 3.073181486

Solving
2.333333334 + y = 3.073181486

Solving for variable 'y'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + y = 3.073181486 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + y = 3.073181486 + -2.333333334
y = 3.073181486 + -2.333333334

Combine like terms: 3.073181486 + -2.333333334 = 0.739848152
y = 0.739848152

Simplifying
y = 0.739848152


Subproblem 2
y + 2.333333334 = -3.073181486

Simplifying
y + 2.333333334 = -3.073181486

Reorder the terms:
2.333333334 + y = -3.073181486

Solving
2.333333334 + y = -3.073181486

Solving for variable 'y'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + y = -3.073181486 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + y = -3.073181486 + -2.333333334
y = -3.073181486 + -2.333333334

Combine like terms: -3.073181486 + -2.333333334 = -5.40651482
y = -5.40651482

Simplifying
y = -5.40651482


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.739848152, -5.40651482}

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