2w^2+19w+35=(w+7)(w+7)

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Solution for 2w^2+19w+35=(w+7)(w+7) equation: 


Simplifying
2w2 + 19w + 35 = (w + 7)(w + 7)

Reorder the terms:
35 + 19w + 2w2 = (w + 7)(w + 7)

Reorder the terms:
35 + 19w + 2w2 = (7 + w)(w + 7)

Reorder the terms:
35 + 19w + 2w2 = (7 + w)(7 + w)

Multiply (7 + w) * (7 + w)
35 + 19w + 2w2 = (7(7 + w) + w(7 + w))
35 + 19w + 2w2 = ((7 * 7 + w * 7) + w(7 + w))
35 + 19w + 2w2 = ((49 + 7w) + w(7 + w))
35 + 19w + 2w2 = (49 + 7w + (7 * w + w * w))
35 + 19w + 2w2 = (49 + 7w + (7w + w2))

Combine like terms: 7w + 7w = 14w
35 + 19w + 2w2 = (49 + 14w + w2)

Solving
35 + 19w + 2w2 = 49 + 14w + w2

Solving for variable 'w'.

Reorder the terms:
35 + -49 + 19w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 35 + -49 = -14
-14 + 19w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 19w + -14w = 5w
-14 + 5w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-14 + 5w + 1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Reorder the terms:
-14 + 5w + 1w2 = 49 + -49 + 14w + -14w + w2 + -1w2

Combine like terms: 49 + -49 = 0
-14 + 5w + 1w2 = 0 + 14w + -14w + w2 + -1w2
-14 + 5w + 1w2 = 14w + -14w + w2 + -1w2

Combine like terms: 14w + -14w = 0
-14 + 5w + 1w2 = 0 + w2 + -1w2
-14 + 5w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-14 + 5w + 1w2 = 0

Factor a trinomial.
(-7 + -1w)(2 + -1w) = 0


Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve:

Simplifying
-7 + -1w = 0

Solving
-7 + -1w = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1w = 0 + 7
-1w = 0 + 7

Combine like terms: 0 + 7 = 7
-1w = 7

Divide each side by '-1'.
w = -7

Simplifying
w = -7

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 = {-7, 2}

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