(4w-2)(1-w)=-38

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Solution for (4w-2)(1-w)=-38 equation: 


Simplifying
(4w + -2)(1 + -1w) = -38

Reorder the terms:
(-2 + 4w)(1 + -1w) = -38

Multiply (-2 + 4w) * (1 + -1w)
(-2(1 + -1w) + 4w * (1 + -1w)) = -38
((1 * -2 + -1w * -2) + 4w * (1 + -1w)) = -38
((-2 + 2w) + 4w * (1 + -1w)) = -38
(-2 + 2w + (1 * 4w + -1w * 4w)) = -38
(-2 + 2w + (4w + -4w2)) = -38

Combine like terms: 2w + 4w = 6w
(-2 + 6w + -4w2) = -38

Solving
-2 + 6w + -4w2 = -38

Solving for variable 'w'.

Reorder the terms:
-2 + 38 + 6w + -4w2 = -38 + 38

Combine like terms: -2 + 38 = 36
36 + 6w + -4w2 = -38 + 38

Combine like terms: -38 + 38 = 0
36 + 6w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 3w + -2w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(18 + 3w + -2w2)' equal to zero and attempt to solve:

Simplifying
18 + 3w + -2w2 = 0

Solving
18 + 3w + -2w2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-9 + -1.5w + w2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -1.5w + 9 + w2 = 0 + 9

Reorder the terms:
-9 + 9 + -1.5w + w2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1.5w + w2 = 0 + 9
-1.5w + w2 = 0 + 9

Combine like terms: 0 + 9 = 9
-1.5w + w2 = 9

The w term is -1.5w.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5w + 0.5625 + w2 = 9 + 0.5625

Reorder the terms:
0.5625 + -1.5w + w2 = 9 + 0.5625

Combine like terms: 9 + 0.5625 = 9.5625
0.5625 + -1.5w + w2 = 9.5625

Factor a perfect square on the left side:
(w + -0.75)(w + -0.75) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(w + -0.75) equal to 3.092329219 and -3.092329219.


Subproblem 1
w + -0.75 = 3.092329219

Simplifying
w + -0.75 = 3.092329219

Reorder the terms:
-0.75 + w = 3.092329219

Solving
-0.75 + w = 3.092329219

Solving for variable 'w'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + w = 3.092329219 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + w = 3.092329219 + 0.75
w = 3.092329219 + 0.75

Combine like terms: 3.092329219 + 0.75 = 3.842329219
w = 3.842329219

Simplifying
w = 3.842329219


Subproblem 2
w + -0.75 = -3.092329219

Simplifying
w + -0.75 = -3.092329219

Reorder the terms:
-0.75 + w = -3.092329219

Solving
-0.75 + w = -3.092329219

Solving for variable 'w'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + w = -3.092329219 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + w = -3.092329219 + 0.75
w = -3.092329219 + 0.75

Combine like terms: -3.092329219 + 0.75 = -2.342329219
w = -2.342329219

Simplifying
w = -2.342329219


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.842329219, -2.342329219}
Solution
w = {3.842329219, -2.342329219}

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