(3w-4)(w)=88

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Solution for (3w-4)(w)=88 equation: 


Simplifying
(3w + -4)(w) = 88

Reorder the terms:
(-4 + 3w)(w) = 88

Reorder the terms for easier multiplication:
w(-4 + 3w) = 88
(-4 * w + 3w * w) = 88
(-4w + 3w2) = 88

Solving
-4w + 3w2 = 88

Solving for variable 'w'.

Reorder the terms:
-88 + -4w + 3w2 = 88 + -88

Combine like terms: 88 + -88 = 0
-88 + -4w + 3w2 = 0

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

Divide each side by '3'.
-29.33333333 + -1.333333333w + w2 = 0

Move the constant term to the right:

Add '29.33333333' to each side of the equation.
-29.33333333 + -1.333333333w + 29.33333333 + w2 = 0 + 29.33333333

Reorder the terms:
-29.33333333 + 29.33333333 + -1.333333333w + w2 = 0 + 29.33333333

Combine like terms: -29.33333333 + 29.33333333 = 0.00000000
0.00000000 + -1.333333333w + w2 = 0 + 29.33333333
-1.333333333w + w2 = 0 + 29.33333333

Combine like terms: 0 + 29.33333333 = 29.33333333
-1.333333333w + w2 = 29.33333333

The w term is -1.333333333w.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333w + 0.4444444442 + w2 = 29.33333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333w + w2 = 29.33333333 + 0.4444444442

Combine like terms: 29.33333333 + 0.4444444442 = 29.7777777742
0.4444444442 + -1.333333333w + w2 = 29.7777777742

Factor a perfect square on the left side:
(w + -0.6666666665)(w + -0.6666666665) = 29.7777777742

Calculate the square root of the right side: 5.456901848

Break this problem into two subproblems by setting 
(w + -0.6666666665) equal to 5.456901848 and -5.456901848.


Subproblem 1
w + -0.6666666665 = 5.456901848

Simplifying
w + -0.6666666665 = 5.456901848

Reorder the terms:
-0.6666666665 + w = 5.456901848

Solving
-0.6666666665 + w = 5.456901848

Solving for variable 'w'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + w = 5.456901848 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + w = 5.456901848 + 0.6666666665
w = 5.456901848 + 0.6666666665

Combine like terms: 5.456901848 + 0.6666666665 = 6.1235685145
w = 6.1235685145

Simplifying
w = 6.1235685145


Subproblem 2
w + -0.6666666665 = -5.456901848

Simplifying
w + -0.6666666665 = -5.456901848

Reorder the terms:
-0.6666666665 + w = -5.456901848

Solving
-0.6666666665 + w = -5.456901848

Solving for variable 'w'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + w = -5.456901848 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + w = -5.456901848 + 0.6666666665
w = -5.456901848 + 0.6666666665

Combine like terms: -5.456901848 + 0.6666666665 = -4.7902351815
w = -4.7902351815

Simplifying
w = -4.7902351815


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.1235685145, -4.7902351815}

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