2w^2+2w+12=(w+3)(w+3)

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Solution for 2w^2+2w+12=(w+3)(w+3) equation: 


Simplifying
2w2 + 2w + 12 = (w + 3)(w + 3)

Reorder the terms:
12 + 2w + 2w2 = (w + 3)(w + 3)

Reorder the terms:
12 + 2w + 2w2 = (3 + w)(w + 3)

Reorder the terms:
12 + 2w + 2w2 = (3 + w)(3 + w)

Multiply (3 + w) * (3 + w)
12 + 2w + 2w2 = (3(3 + w) + w(3 + w))
12 + 2w + 2w2 = ((3 * 3 + w * 3) + w(3 + w))
12 + 2w + 2w2 = ((9 + 3w) + w(3 + w))
12 + 2w + 2w2 = (9 + 3w + (3 * w + w * w))
12 + 2w + 2w2 = (9 + 3w + (3w + w2))

Combine like terms: 3w + 3w = 6w
12 + 2w + 2w2 = (9 + 6w + w2)

Solving
12 + 2w + 2w2 = 9 + 6w + w2

Solving for variable 'w'.

Reorder the terms:
12 + -9 + 2w + -6w + 2w2 + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Combine like terms: 12 + -9 = 3
3 + 2w + -6w + 2w2 + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Combine like terms: 2w + -6w = -4w
3 + -4w + 2w2 + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
3 + -4w + 1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Reorder the terms:
3 + -4w + 1w2 = 9 + -9 + 6w + -6w + w2 + -1w2

Combine like terms: 9 + -9 = 0
3 + -4w + 1w2 = 0 + 6w + -6w + w2 + -1w2
3 + -4w + 1w2 = 6w + -6w + w2 + -1w2

Combine like terms: 6w + -6w = 0
3 + -4w + 1w2 = 0 + w2 + -1w2
3 + -4w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
3 + -4w + 1w2 = 0

Factor a trinomial.
(1 + -1w)(3 + -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 '(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 = {1, 3}

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