2w^2+10w+28=(w+6)(w+6)

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Solution for 2w^2+10w+28=(w+6)(w+6) equation: 


Simplifying
2w2 + 10w + 28 = (w + 6)(w + 6)

Reorder the terms:
28 + 10w + 2w2 = (w + 6)(w + 6)

Reorder the terms:
28 + 10w + 2w2 = (6 + w)(w + 6)

Reorder the terms:
28 + 10w + 2w2 = (6 + w)(6 + w)

Multiply (6 + w) * (6 + w)
28 + 10w + 2w2 = (6(6 + w) + w(6 + w))
28 + 10w + 2w2 = ((6 * 6 + w * 6) + w(6 + w))
28 + 10w + 2w2 = ((36 + 6w) + w(6 + w))
28 + 10w + 2w2 = (36 + 6w + (6 * w + w * w))
28 + 10w + 2w2 = (36 + 6w + (6w + w2))

Combine like terms: 6w + 6w = 12w
28 + 10w + 2w2 = (36 + 12w + w2)

Solving
28 + 10w + 2w2 = 36 + 12w + w2

Solving for variable 'w'.

Reorder the terms:
28 + -36 + 10w + -12w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 28 + -36 = -8
-8 + 10w + -12w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 10w + -12w = -2w
-8 + -2w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

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

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

Combine like terms: 36 + -36 = 0
-8 + -2w + 1w2 = 0 + 12w + -12w + w2 + -1w2
-8 + -2w + 1w2 = 12w + -12w + w2 + -1w2

Combine like terms: 12w + -12w = 0
-8 + -2w + 1w2 = 0 + w2 + -1w2
-8 + -2w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-8 + -2w + 1w2 = 0

Factor a trinomial.
(-2 + -1w)(4 + -1w) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

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

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

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-2, 4}

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