2w^2+8w+31=(w+6)(w+6)

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Solution for 2w^2+8w+31=(w+6)(w+6) equation: 


Simplifying
2w2 + 8w + 31 = (w + 6)(w + 6)

Reorder the terms:
31 + 8w + 2w2 = (w + 6)(w + 6)

Reorder the terms:
31 + 8w + 2w2 = (6 + w)(w + 6)

Reorder the terms:
31 + 8w + 2w2 = (6 + w)(6 + w)

Multiply (6 + w) * (6 + w)
31 + 8w + 2w2 = (6(6 + w) + w(6 + w))
31 + 8w + 2w2 = ((6 * 6 + w * 6) + w(6 + w))
31 + 8w + 2w2 = ((36 + 6w) + w(6 + w))
31 + 8w + 2w2 = (36 + 6w + (6 * w + w * w))
31 + 8w + 2w2 = (36 + 6w + (6w + w2))

Combine like terms: 6w + 6w = 12w
31 + 8w + 2w2 = (36 + 12w + w2)

Solving
31 + 8w + 2w2 = 36 + 12w + w2

Solving for variable 'w'.

Reorder the terms:
31 + -36 + 8w + -12w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 31 + -36 = -5
-5 + 8w + -12w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 8w + -12w = -4w
-5 + -4w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-5 + -4w + 1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Reorder the terms:
-5 + -4w + 1w2 = 36 + -36 + 12w + -12w + w2 + -1w2

Combine like terms: 36 + -36 = 0
-5 + -4w + 1w2 = 0 + 12w + -12w + w2 + -1w2
-5 + -4w + 1w2 = 12w + -12w + w2 + -1w2

Combine like terms: 12w + -12w = 0
-5 + -4w + 1w2 = 0 + w2 + -1w2
-5 + -4w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-5 + -4w + 1w2 = 0

Factor a trinomial.
(-1 + -1w)(5 + -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 '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-1, 5}

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