-3y^2-26y-45=0

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Solution for -3y^2-26y-45=0 equation: 


Simplifying
-3y2 + -26y + -45 = 0

Reorder the terms:
-45 + -26y + -3y2 = 0

Solving
-45 + -26y + -3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(45 + 26y + 3y2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(45 + 26y + 3y2)' equal to zero and attempt to solve:

Simplifying
45 + 26y + 3y2 = 0

Solving
45 + 26y + 3y2 = 0

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

Divide each side by '3'.
15 + 8.666666667y + y2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 8.666666667y + -15 + y2 = 0 + -15

Reorder the terms:
15 + -15 + 8.666666667y + y2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 8.666666667y + y2 = 0 + -15
8.666666667y + y2 = 0 + -15

Combine like terms: 0 + -15 = -15
8.666666667y + y2 = -15

The y term is 8.666666667y.  Take half its coefficient (4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
8.666666667y + 18.77777778 + y2 = -15 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667y + y2 = -15 + 18.77777778

Combine like terms: -15 + 18.77777778 = 3.77777778
18.77777778 + 8.666666667y + y2 = 3.77777778

Factor a perfect square on the left side:
(y + 4.333333334)(y + 4.333333334) = 3.77777778

Calculate the square root of the right side: 1.943650632

Break this problem into two subproblems by setting 
(y + 4.333333334) equal to 1.943650632 and -1.943650632.


Subproblem 1
y + 4.333333334 = 1.943650632

Simplifying
y + 4.333333334 = 1.943650632

Reorder the terms:
4.333333334 + y = 1.943650632

Solving
4.333333334 + y = 1.943650632

Solving for variable 'y'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + y = 1.943650632 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + y = 1.943650632 + -4.333333334
y = 1.943650632 + -4.333333334

Combine like terms: 1.943650632 + -4.333333334 = -2.389682702
y = -2.389682702

Simplifying
y = -2.389682702


Subproblem 2
y + 4.333333334 = -1.943650632

Simplifying
y + 4.333333334 = -1.943650632

Reorder the terms:
4.333333334 + y = -1.943650632

Solving
4.333333334 + y = -1.943650632

Solving for variable 'y'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + y = -1.943650632 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + y = -1.943650632 + -4.333333334
y = -1.943650632 + -4.333333334

Combine like terms: -1.943650632 + -4.333333334 = -6.276983966
y = -6.276983966

Simplifying
y = -6.276983966


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.389682702, -6.276983966}
Solution
y = {-2.389682702, -6.276983966}

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