2w^2+16w+46=(w+7)(w+7)

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Solution for 2w^2+16w+46=(w+7)(w+7) equation: 


Simplifying
2w2 + 16w + 46 = (w + 7)(w + 7)

Reorder the terms:
46 + 16w + 2w2 = (w + 7)(w + 7)

Reorder the terms:
46 + 16w + 2w2 = (7 + w)(w + 7)

Reorder the terms:
46 + 16w + 2w2 = (7 + w)(7 + w)

Multiply (7 + w) * (7 + w)
46 + 16w + 2w2 = (7(7 + w) + w(7 + w))
46 + 16w + 2w2 = ((7 * 7 + w * 7) + w(7 + w))
46 + 16w + 2w2 = ((49 + 7w) + w(7 + w))
46 + 16w + 2w2 = (49 + 7w + (7 * w + w * w))
46 + 16w + 2w2 = (49 + 7w + (7w + w2))

Combine like terms: 7w + 7w = 14w
46 + 16w + 2w2 = (49 + 14w + w2)

Solving
46 + 16w + 2w2 = 49 + 14w + w2

Solving for variable 'w'.

Reorder the terms:
46 + -49 + 16w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 46 + -49 = -3
-3 + 16w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 16w + -14w = 2w
-3 + 2w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-3 + 2w + 1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Reorder the terms:
-3 + 2w + 1w2 = 49 + -49 + 14w + -14w + w2 + -1w2

Combine like terms: 49 + -49 = 0
-3 + 2w + 1w2 = 0 + 14w + -14w + w2 + -1w2
-3 + 2w + 1w2 = 14w + -14w + w2 + -1w2

Combine like terms: 14w + -14w = 0
-3 + 2w + 1w2 = 0 + w2 + -1w2
-3 + 2w + 1w2 = w2 + -1w2

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

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


Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 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 + -1w = 0 + 3

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

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

Divide each side by '-1'.
w = -3

Simplifying
w = -3

Subproblem 2
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
Solution
w = {-3, 1}

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