2w^2+9w+38=(w+6)(w+6)

Solution for 2w^2+9w+38=(w+6)(w+6) equation:

Simplifying
2w2 + 9w + 38 = (w + 6)(w + 6)

Reorder the terms:
38 + 9w + 2w2 = (w + 6)(w + 6)

Reorder the terms:
38 + 9w + 2w2 = (6 + w)(w + 6)

Reorder the terms:
38 + 9w + 2w2 = (6 + w)(6 + w)

Multiply (6 + w) * (6 + w)
38 + 9w + 2w2 = (6(6 + w) + w(6 + w))
38 + 9w + 2w2 = ((6 * 6 + w * 6) + w(6 + w))
38 + 9w + 2w2 = ((36 + 6w) + w(6 + w))
38 + 9w + 2w2 = (36 + 6w + (6 * w + w * w))
38 + 9w + 2w2 = (36 + 6w + (6w + w2))

Combine like terms: 6w + 6w = 12w
38 + 9w + 2w2 = (36 + 12w + w2)

Solving
38 + 9w + 2w2 = 36 + 12w + w2

Solving for variable 'w'.

Reorder the terms:
38 + -36 + 9w + -12w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 38 + -36 = 2
2 + 9w + -12w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 9w + -12w = -3w
2 + -3w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
2 + -3w + 1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Reorder the terms:
2 + -3w + 1w2 = 36 + -36 + 12w + -12w + w2 + -1w2

Combine like terms: 36 + -36 = 0
2 + -3w + 1w2 = 0 + 12w + -12w + w2 + -1w2
2 + -3w + 1w2 = 12w + -12w + w2 + -1w2

Combine like terms: 12w + -12w = 0
2 + -3w + 1w2 = 0 + w2 + -1w2
2 + -3w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
2 + -3w + 1w2 = 0

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

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1
Subproblem 2
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
Solution
w = {1, 2}