(w+4)(w+4)=(2w*2w)+11w-2

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Solution for (w+4)(w+4)=(2w*2w)+11w-2 equation: 


Simplifying
(w + 4)(w + 4) = (2w * 2w) + 11w + -2

Reorder the terms:
(4 + w)(w + 4) = (2w * 2w) + 11w + -2

Reorder the terms:
(4 + w)(4 + w) = (2w * 2w) + 11w + -2

Multiply (4 + w) * (4 + w)
(4(4 + w) + w(4 + w)) = (2w * 2w) + 11w + -2
((4 * 4 + w * 4) + w(4 + w)) = (2w * 2w) + 11w + -2
((16 + 4w) + w(4 + w)) = (2w * 2w) + 11w + -2
(16 + 4w + (4 * w + w * w)) = (2w * 2w) + 11w + -2
(16 + 4w + (4w + w2)) = (2w * 2w) + 11w + -2

Combine like terms: 4w + 4w = 8w
(16 + 8w + w2) = (2w * 2w) + 11w + -2

Reorder the terms for easier multiplication:
16 + 8w + w2 = (2 * 2w * w) + 11w + -2

Multiply 2 * 2
16 + 8w + w2 = (4w * w) + 11w + -2

Multiply w * w
16 + 8w + w2 = (4w2) + 11w + -2

Reorder the terms:
16 + 8w + w2 = -2 + 11w + (4w2)

Solving
16 + 8w + w2 = -2 + 11w + (4w2)

Solving for variable 'w'.

Reorder the terms:
16 + 2 + 8w + -11w + w2 + (-4w2) = -2 + 11w + (4w2) + 2 + -11w + (-4w2)

Combine like terms: 16 + 2 = 18
18 + 8w + -11w + w2 + (-4w2) = -2 + 11w + (4w2) + 2 + -11w + (-4w2)

Combine like terms: 8w + -11w = -3w
18 + -3w + w2 + (-4w2) = -2 + 11w + (4w2) + 2 + -11w + (-4w2)

Combine like terms: w2 + (-4w2) = -3w2
18 + -3w + -3w2 = -2 + 11w + (4w2) + 2 + -11w + (-4w2)

Reorder the terms:
18 + -3w + -3w2 = -2 + 2 + 11w + -11w + (4w2) + (-4w2)

Combine like terms: -2 + 2 = 0
18 + -3w + -3w2 = 0 + 11w + -11w + (4w2) + (-4w2)
18 + -3w + -3w2 = 11w + -11w + (4w2) + (-4w2)

Combine like terms: 11w + -11w = 0
18 + -3w + -3w2 = 0 + (4w2) + (-4w2)
18 + -3w + -3w2 = (4w2) + (-4w2)

Combine like terms: (4w2) + (-4w2) = 0
18 + -3w + -3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -1w + -1w2) = 0

Factor a trinomial.
3((2 + -1w)(3 + w)) = 0

Ignore the factor 3.

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2

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

Simplifying
3 + w = 0

Solving
3 + w = 0

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

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
Solution
w = {2, -3}

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