7(6-w)-3w(2+w)=

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Solution for 7(6-w)-3w(2+w)= equation: 


Simplifying
7(6 + -1w) + -3w(2 + w) = 0
(6 * 7 + -1w * 7) + -3w(2 + w) = 0
(42 + -7w) + -3w(2 + w) = 0
42 + -7w + (2 * -3w + w * -3w) = 0
42 + -7w + (-6w + -3w2) = 0

Combine like terms: -7w + -6w = -13w
42 + -13w + -3w2 = 0

Solving
42 + -13w + -3w2 = 0

Solving for variable 'w'.

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

Divide each side by '-3'.
-14 + 4.333333333w + w2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 4.333333333w + 14 + w2 = 0 + 14

Reorder the terms:
-14 + 14 + 4.333333333w + w2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 4.333333333w + w2 = 0 + 14
4.333333333w + w2 = 0 + 14

Combine like terms: 0 + 14 = 14
4.333333333w + w2 = 14

The w term is 4.333333333w.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333w + 4.694444446 + w2 = 14 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333w + w2 = 14 + 4.694444446

Combine like terms: 14 + 4.694444446 = 18.694444446
4.694444446 + 4.333333333w + w2 = 18.694444446

Factor a perfect square on the left side:
(w + 2.166666667)(w + 2.166666667) = 18.694444446

Calculate the square root of the right side: 4.323707257

Break this problem into two subproblems by setting 
(w + 2.166666667) equal to 4.323707257 and -4.323707257.


Subproblem 1
w + 2.166666667 = 4.323707257

Simplifying
w + 2.166666667 = 4.323707257

Reorder the terms:
2.166666667 + w = 4.323707257

Solving
2.166666667 + w = 4.323707257

Solving for variable 'w'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + w = 4.323707257 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + w = 4.323707257 + -2.166666667
w = 4.323707257 + -2.166666667

Combine like terms: 4.323707257 + -2.166666667 = 2.15704059
w = 2.15704059

Simplifying
w = 2.15704059


Subproblem 2
w + 2.166666667 = -4.323707257

Simplifying
w + 2.166666667 = -4.323707257

Reorder the terms:
2.166666667 + w = -4.323707257

Solving
2.166666667 + w = -4.323707257

Solving for variable 'w'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + w = -4.323707257 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + w = -4.323707257 + -2.166666667
w = -4.323707257 + -2.166666667

Combine like terms: -4.323707257 + -2.166666667 = -6.490373924
w = -6.490373924

Simplifying
w = -6.490373924


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.15704059, -6.490373924}

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