129=(3w+3)w

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Solution for 129=(3w+3)w equation: 


Simplifying
129 = (3w + 3) * w

Reorder the terms:
129 = (3 + 3w) * w

Reorder the terms for easier multiplication:
129 = w(3 + 3w)
129 = (3 * w + 3w * w)
129 = (3w + 3w2)

Solving
129 = 3w + 3w2

Solving for variable 'w'.

Reorder the terms:
129 + -3w + -3w2 = 3w + -3w + 3w2 + -3w2

Combine like terms: 3w + -3w = 0
129 + -3w + -3w2 = 0 + 3w2 + -3w2
129 + -3w + -3w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
129 + -3w + -3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(43 + -1w + -1w2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(43 + -1w + -1w2)' equal to zero and attempt to solve:

Simplifying
43 + -1w + -1w2 = 0

Solving
43 + -1w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-43 + w + w2 = 0

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + w + 43 + w2 = 0 + 43

Reorder the terms:
-43 + 43 + w + w2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + w + w2 = 0 + 43
w + w2 = 0 + 43

Combine like terms: 0 + 43 = 43
w + w2 = 43

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + w2 = 43 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + w2 = 43 + 0.25

Combine like terms: 43 + 0.25 = 43.25
1.25 + w2 = 43.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 43.25

Calculate the square root of the right side: 6.576473219

Break this problem into two subproblems by setting 
(w + 0.5) equal to 6.576473219 and -6.576473219.


Subproblem 1
w + 0.5 = 6.576473219

Simplifying
w + 0.5 = 6.576473219

Reorder the terms:
0.5 + w = 6.576473219

Solving
0.5 + w = 6.576473219

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 6.576473219 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 6.576473219 + -0.5
w = 6.576473219 + -0.5

Combine like terms: 6.576473219 + -0.5 = 6.076473219
w = 6.076473219

Simplifying
w = 6.076473219


Subproblem 2
w + 0.5 = -6.576473219

Simplifying
w + 0.5 = -6.576473219

Reorder the terms:
0.5 + w = -6.576473219

Solving
0.5 + w = -6.576473219

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -6.576473219 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -6.576473219 + -0.5
w = -6.576473219 + -0.5

Combine like terms: -6.576473219 + -0.5 = -7.076473219
w = -7.076473219

Simplifying
w = -7.076473219


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.076473219, -7.076473219}
Solution
w = {6.076473219, -7.076473219}

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