(2w-6.4)(4w-8.4)=0

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Solution for (2w-6.4)(4w-8.4)=0 equation:


Simplifying
(2w + -6.4)(4w + -8.4) = 0

Reorder the terms:
(-6.4 + 2w)(4w + -8.4) = 0

Reorder the terms:
(-6.4 + 2w)(-8.4 + 4w) = 0

Multiply (-6.4 + 2w) * (-8.4 + 4w)
(-6.4(-8.4 + 4w) + 2w * (-8.4 + 4w)) = 0
((-8.4 * -6.4 + 4w * -6.4) + 2w * (-8.4 + 4w)) = 0
((53.76 + -25.6w) + 2w * (-8.4 + 4w)) = 0
(53.76 + -25.6w + (-8.4 * 2w + 4w * 2w)) = 0
(53.76 + -25.6w + (-16.8w + 8w2)) = 0

Combine like terms: -25.6w + -16.8w = -42.4w
(53.76 + -42.4w + 8w2) = 0

Solving
53.76 + -42.4w + 8w2 = 0

Solving for variable 'w'.

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

Divide each side by '8'.
6.72 + -5.3w + w2 = 0

Move the constant term to the right:

Add '-6.72' to each side of the equation.
6.72 + -5.3w + -6.72 + w2 = 0 + -6.72

Reorder the terms:
6.72 + -6.72 + -5.3w + w2 = 0 + -6.72

Combine like terms: 6.72 + -6.72 = 0.00
0.00 + -5.3w + w2 = 0 + -6.72
-5.3w + w2 = 0 + -6.72

Combine like terms: 0 + -6.72 = -6.72
-5.3w + w2 = -6.72

The w term is -5.3w.  Take half its coefficient (-2.65).
Square it (7.0225) and add it to both sides.

Add '7.0225' to each side of the equation.
-5.3w + 7.0225 + w2 = -6.72 + 7.0225

Reorder the terms:
7.0225 + -5.3w + w2 = -6.72 + 7.0225

Combine like terms: -6.72 + 7.0225 = 0.3025
7.0225 + -5.3w + w2 = 0.3025

Factor a perfect square on the left side:
(w + -2.65)(w + -2.65) = 0.3025

Calculate the square root of the right side: 0.55

Break this problem into two subproblems by setting 
(w + -2.65) equal to 0.55 and -0.55.

Subproblem 1

w + -2.65 = 0.55 Simplifying w + -2.65 = 0.55 Reorder the terms: -2.65 + w = 0.55 Solving -2.65 + w = 0.55 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.65' to each side of the equation. -2.65 + 2.65 + w = 0.55 + 2.65 Combine like terms: -2.65 + 2.65 = 0.00 0.00 + w = 0.55 + 2.65 w = 0.55 + 2.65 Combine like terms: 0.55 + 2.65 = 3.2 w = 3.2 Simplifying w = 3.2

Subproblem 2

w + -2.65 = -0.55 Simplifying w + -2.65 = -0.55 Reorder the terms: -2.65 + w = -0.55 Solving -2.65 + w = -0.55 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.65' to each side of the equation. -2.65 + 2.65 + w = -0.55 + 2.65 Combine like terms: -2.65 + 2.65 = 0.00 0.00 + w = -0.55 + 2.65 w = -0.55 + 2.65 Combine like terms: -0.55 + 2.65 = 2.1 w = 2.1 Simplifying w = 2.1

Solution

The solution to the problem is based on the solutions from the subproblems. w = {3.2, 2.1}

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