3w^2+27w-120=0

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Solution for 3w^2+27w-120=0 equation: 


Simplifying
3w2 + 27w + -120 = 0

Reorder the terms:
-120 + 27w + 3w2 = 0

Solving
-120 + 27w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + 9w + w2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-40 + 9w + w2)' equal to zero and attempt to solve:

Simplifying
-40 + 9w + w2 = 0

Solving
-40 + 9w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 9w + 40 + w2 = 0 + 40

Reorder the terms:
-40 + 40 + 9w + w2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 9w + w2 = 0 + 40
9w + w2 = 0 + 40

Combine like terms: 0 + 40 = 40
9w + w2 = 40

The w term is 9w.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9w + 20.25 + w2 = 40 + 20.25

Reorder the terms:
20.25 + 9w + w2 = 40 + 20.25

Combine like terms: 40 + 20.25 = 60.25
20.25 + 9w + w2 = 60.25

Factor a perfect square on the left side:
(w + 4.5)(w + 4.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(w + 4.5) equal to 7.762087348 and -7.762087348.


Subproblem 1
w + 4.5 = 7.762087348

Simplifying
w + 4.5 = 7.762087348

Reorder the terms:
4.5 + w = 7.762087348

Solving
4.5 + w = 7.762087348

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = 7.762087348 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = 7.762087348 + -4.5
w = 7.762087348 + -4.5

Combine like terms: 7.762087348 + -4.5 = 3.262087348
w = 3.262087348

Simplifying
w = 3.262087348


Subproblem 2
w + 4.5 = -7.762087348

Simplifying
w + 4.5 = -7.762087348

Reorder the terms:
4.5 + w = -7.762087348

Solving
4.5 + w = -7.762087348

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = -7.762087348 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = -7.762087348 + -4.5
w = -7.762087348 + -4.5

Combine like terms: -7.762087348 + -4.5 = -12.262087348
w = -12.262087348

Simplifying
w = -12.262087348


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.262087348, -12.262087348}
Solution
w = {3.262087348, -12.262087348}

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