(2w+18)(w-4)=168

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Solution for (2w+18)(w-4)=168 equation: 


Simplifying
(2w + 18)(w + -4) = 168

Reorder the terms:
(18 + 2w)(w + -4) = 168

Reorder the terms:
(18 + 2w)(-4 + w) = 168

Multiply (18 + 2w) * (-4 + w)
(18(-4 + w) + 2w * (-4 + w)) = 168
((-4 * 18 + w * 18) + 2w * (-4 + w)) = 168
((-72 + 18w) + 2w * (-4 + w)) = 168
(-72 + 18w + (-4 * 2w + w * 2w)) = 168
(-72 + 18w + (-8w + 2w2)) = 168

Combine like terms: 18w + -8w = 10w
(-72 + 10w + 2w2) = 168

Solving
-72 + 10w + 2w2 = 168

Solving for variable 'w'.

Reorder the terms:
-72 + -168 + 10w + 2w2 = 168 + -168

Combine like terms: -72 + -168 = -240
-240 + 10w + 2w2 = 168 + -168

Combine like terms: 168 + -168 = 0
-240 + 10w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-120 + 5w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-120 + 5w + w2)' equal to zero and attempt to solve:

Simplifying
-120 + 5w + w2 = 0

Solving
-120 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 5w + 120 + w2 = 0 + 120

Reorder the terms:
-120 + 120 + 5w + w2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 5w + w2 = 0 + 120
5w + w2 = 0 + 120

Combine like terms: 0 + 120 = 120
5w + w2 = 120

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 120 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 120 + 6.25

Combine like terms: 120 + 6.25 = 126.25
6.25 + 5w + w2 = 126.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 126.25

Calculate the square root of the right side: 11.236102527

Break this problem into two subproblems by setting 
(w + 2.5) equal to 11.236102527 and -11.236102527.


Subproblem 1
w + 2.5 = 11.236102527

Simplifying
w + 2.5 = 11.236102527

Reorder the terms:
2.5 + w = 11.236102527

Solving
2.5 + w = 11.236102527

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 11.236102527 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 11.236102527 + -2.5
w = 11.236102527 + -2.5

Combine like terms: 11.236102527 + -2.5 = 8.736102527
w = 8.736102527

Simplifying
w = 8.736102527


Subproblem 2
w + 2.5 = -11.236102527

Simplifying
w + 2.5 = -11.236102527

Reorder the terms:
2.5 + w = -11.236102527

Solving
2.5 + w = -11.236102527

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -11.236102527 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -11.236102527 + -2.5
w = -11.236102527 + -2.5

Combine like terms: -11.236102527 + -2.5 = -13.736102527
w = -13.736102527

Simplifying
w = -13.736102527


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.736102527, -13.736102527}
Solution
w = {8.736102527, -13.736102527}

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