2w^2+4w-14=(w+1)(w+1)

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Solution for 2w^2+4w-14=(w+1)(w+1) equation: 


Simplifying
2w2 + 4w + -14 = (w + 1)(w + 1)

Reorder the terms:
-14 + 4w + 2w2 = (w + 1)(w + 1)

Reorder the terms:
-14 + 4w + 2w2 = (1 + w)(w + 1)

Reorder the terms:
-14 + 4w + 2w2 = (1 + w)(1 + w)

Multiply (1 + w) * (1 + w)
-14 + 4w + 2w2 = (1(1 + w) + w(1 + w))
-14 + 4w + 2w2 = ((1 * 1 + w * 1) + w(1 + w))
-14 + 4w + 2w2 = ((1 + 1w) + w(1 + w))
-14 + 4w + 2w2 = (1 + 1w + (1 * w + w * w))
-14 + 4w + 2w2 = (1 + 1w + (1w + w2))

Combine like terms: 1w + 1w = 2w
-14 + 4w + 2w2 = (1 + 2w + w2)

Solving
-14 + 4w + 2w2 = 1 + 2w + w2

Solving for variable 'w'.

Reorder the terms:
-14 + -1 + 4w + -2w + 2w2 + -1w2 = 1 + 2w + w2 + -1 + -2w + -1w2

Combine like terms: -14 + -1 = -15
-15 + 4w + -2w + 2w2 + -1w2 = 1 + 2w + w2 + -1 + -2w + -1w2

Combine like terms: 4w + -2w = 2w
-15 + 2w + 2w2 + -1w2 = 1 + 2w + w2 + -1 + -2w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-15 + 2w + 1w2 = 1 + 2w + w2 + -1 + -2w + -1w2

Reorder the terms:
-15 + 2w + 1w2 = 1 + -1 + 2w + -2w + w2 + -1w2

Combine like terms: 1 + -1 = 0
-15 + 2w + 1w2 = 0 + 2w + -2w + w2 + -1w2
-15 + 2w + 1w2 = 2w + -2w + w2 + -1w2

Combine like terms: 2w + -2w = 0
-15 + 2w + 1w2 = 0 + w2 + -1w2
-15 + 2w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-15 + 2w + 1w2 = 0

Factor a trinomial.
(-5 + -1w)(3 + -1w) = 0


Subproblem 1
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

Subproblem 2
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
Solution
w = {-5, 3}

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