(w+4)(w+4)=2w^2+17w+34

Solution for (w+4)(w+4)=2w^2+17w+34 equation:

Simplifying
(w + 4)(w + 4) = 2w2 + 17w + 34

Reorder the terms:
(4 + w)(w + 4) = 2w2 + 17w + 34

Reorder the terms:
(4 + w)(4 + w) = 2w2 + 17w + 34

Multiply (4 + w) * (4 + w)
(4(4 + w) + w(4 + w)) = 2w2 + 17w + 34
((4 * 4 + w * 4) + w(4 + w)) = 2w2 + 17w + 34
((16 + 4w) + w(4 + w)) = 2w2 + 17w + 34
(16 + 4w + (4 * w + w * w)) = 2w2 + 17w + 34
(16 + 4w + (4w + w2)) = 2w2 + 17w + 34

Combine like terms: 4w + 4w = 8w
(16 + 8w + w2) = 2w2 + 17w + 34

Reorder the terms:
16 + 8w + w2 = 34 + 17w + 2w2

Solving
16 + 8w + w2 = 34 + 17w + 2w2

Solving for variable 'w'.

Reorder the terms:
16 + -34 + 8w + -17w + w2 + -2w2 = 34 + 17w + 2w2 + -34 + -17w + -2w2

Combine like terms: 16 + -34 = -18
-18 + 8w + -17w + w2 + -2w2 = 34 + 17w + 2w2 + -34 + -17w + -2w2

Combine like terms: 8w + -17w = -9w
-18 + -9w + w2 + -2w2 = 34 + 17w + 2w2 + -34 + -17w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-18 + -9w + -1w2 = 34 + 17w + 2w2 + -34 + -17w + -2w2

Reorder the terms:
-18 + -9w + -1w2 = 34 + -34 + 17w + -17w + 2w2 + -2w2

Combine like terms: 34 + -34 = 0
-18 + -9w + -1w2 = 0 + 17w + -17w + 2w2 + -2w2
-18 + -9w + -1w2 = 17w + -17w + 2w2 + -2w2

Combine like terms: 17w + -17w = 0
-18 + -9w + -1w2 = 0 + 2w2 + -2w2
-18 + -9w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-18 + -9w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 9w + w2) = 0

Factor a trinomial.
-1((6 + w)(3 + w)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
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 = {-6, -3}