7w+14=-8(w+2)(w+1)+5w+5

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Solution for 7w+14=-8(w+2)(w+1)+5w+5 equation: 


Simplifying
7w + 14 = -8(w + 2)(w + 1) + 5w + 5

Reorder the terms:
14 + 7w = -8(w + 2)(w + 1) + 5w + 5

Reorder the terms:
14 + 7w = -8(2 + w)(w + 1) + 5w + 5

Reorder the terms:
14 + 7w = -8(2 + w)(1 + w) + 5w + 5

Multiply (2 + w) * (1 + w)
14 + 7w = -8(2(1 + w) + w(1 + w)) + 5w + 5
14 + 7w = -8((1 * 2 + w * 2) + w(1 + w)) + 5w + 5
14 + 7w = -8((2 + 2w) + w(1 + w)) + 5w + 5
14 + 7w = -8(2 + 2w + (1 * w + w * w)) + 5w + 5
14 + 7w = -8(2 + 2w + (1w + w2)) + 5w + 5

Combine like terms: 2w + 1w = 3w
14 + 7w = -8(2 + 3w + w2) + 5w + 5
14 + 7w = (2 * -8 + 3w * -8 + w2 * -8) + 5w + 5
14 + 7w = (-16 + -24w + -8w2) + 5w + 5

Reorder the terms:
14 + 7w = -16 + 5 + -24w + 5w + -8w2

Combine like terms: -16 + 5 = -11
14 + 7w = -11 + -24w + 5w + -8w2

Combine like terms: -24w + 5w = -19w
14 + 7w = -11 + -19w + -8w2

Solving
14 + 7w = -11 + -19w + -8w2

Solving for variable 'w'.

Reorder the terms:
14 + 11 + 7w + 19w + 8w2 = -11 + -19w + -8w2 + 11 + 19w + 8w2

Combine like terms: 14 + 11 = 25
25 + 7w + 19w + 8w2 = -11 + -19w + -8w2 + 11 + 19w + 8w2

Combine like terms: 7w + 19w = 26w
25 + 26w + 8w2 = -11 + -19w + -8w2 + 11 + 19w + 8w2

Reorder the terms:
25 + 26w + 8w2 = -11 + 11 + -19w + 19w + -8w2 + 8w2

Combine like terms: -11 + 11 = 0
25 + 26w + 8w2 = 0 + -19w + 19w + -8w2 + 8w2
25 + 26w + 8w2 = -19w + 19w + -8w2 + 8w2

Combine like terms: -19w + 19w = 0
25 + 26w + 8w2 = 0 + -8w2 + 8w2
25 + 26w + 8w2 = -8w2 + 8w2

Combine like terms: -8w2 + 8w2 = 0
25 + 26w + 8w2 = 0

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

Divide each side by '8'.
3.125 + 3.25w + w2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + 3.25w + -3.125 + w2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + 3.25w + w2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + 3.25w + w2 = 0 + -3.125
3.25w + w2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
3.25w + w2 = -3.125

The w term is 3.25w.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25w + 2.640625 + w2 = -3.125 + 2.640625

Reorder the terms:
2.640625 + 3.25w + w2 = -3.125 + 2.640625

Combine like terms: -3.125 + 2.640625 = -0.484375
2.640625 + 3.25w + w2 = -0.484375

Factor a perfect square on the left side:
(w + 1.625)(w + 1.625) = -0.484375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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