(y)(y)+3y-36=0

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Solution for (y)(y)+3y-36=0 equation: 


Simplifying
(y)(y) + 3y + -36 = 0

Multiply y * y
y2 + 3y + -36 = 0

Reorder the terms:
-36 + 3y + y2 = 0

Solving
-36 + 3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 3y + 36 + y2 = 0 + 36

Reorder the terms:
-36 + 36 + 3y + y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 3y + y2 = 0 + 36
3y + y2 = 0 + 36

Combine like terms: 0 + 36 = 36
3y + y2 = 36

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 36 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 36 + 2.25

Combine like terms: 36 + 2.25 = 38.25
2.25 + 3y + y2 = 38.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(y + 1.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
y + 1.5 = 6.184658438

Simplifying
y + 1.5 = 6.184658438

Reorder the terms:
1.5 + y = 6.184658438

Solving
1.5 + y = 6.184658438

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 6.184658438 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 6.184658438 + -1.5
y = 6.184658438 + -1.5

Combine like terms: 6.184658438 + -1.5 = 4.684658438
y = 4.684658438

Simplifying
y = 4.684658438


Subproblem 2
y + 1.5 = -6.184658438

Simplifying
y + 1.5 = -6.184658438

Reorder the terms:
1.5 + y = -6.184658438

Solving
1.5 + y = -6.184658438

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -6.184658438 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -6.184658438 + -1.5
y = -6.184658438 + -1.5

Combine like terms: -6.184658438 + -1.5 = -7.684658438
y = -7.684658438

Simplifying
y = -7.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.684658438, -7.684658438}

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