(w+4)(w+4)=2w^2+2w+25

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Solution for (w+4)(w+4)=2w^2+2w+25 equation: 


Simplifying
(w + 4)(w + 4) = 2w2 + 2w + 25

Reorder the terms:
(4 + w)(w + 4) = 2w2 + 2w + 25

Reorder the terms:
(4 + w)(4 + w) = 2w2 + 2w + 25

Multiply (4 + w) * (4 + w)
(4(4 + w) + w(4 + w)) = 2w2 + 2w + 25
((4 * 4 + w * 4) + w(4 + w)) = 2w2 + 2w + 25
((16 + 4w) + w(4 + w)) = 2w2 + 2w + 25
(16 + 4w + (4 * w + w * w)) = 2w2 + 2w + 25
(16 + 4w + (4w + w2)) = 2w2 + 2w + 25

Combine like terms: 4w + 4w = 8w
(16 + 8w + w2) = 2w2 + 2w + 25

Reorder the terms:
16 + 8w + w2 = 25 + 2w + 2w2

Solving
16 + 8w + w2 = 25 + 2w + 2w2

Solving for variable 'w'.

Reorder the terms:
16 + -25 + 8w + -2w + w2 + -2w2 = 25 + 2w + 2w2 + -25 + -2w + -2w2

Combine like terms: 16 + -25 = -9
-9 + 8w + -2w + w2 + -2w2 = 25 + 2w + 2w2 + -25 + -2w + -2w2

Combine like terms: 8w + -2w = 6w
-9 + 6w + w2 + -2w2 = 25 + 2w + 2w2 + -25 + -2w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-9 + 6w + -1w2 = 25 + 2w + 2w2 + -25 + -2w + -2w2

Reorder the terms:
-9 + 6w + -1w2 = 25 + -25 + 2w + -2w + 2w2 + -2w2

Combine like terms: 25 + -25 = 0
-9 + 6w + -1w2 = 0 + 2w + -2w + 2w2 + -2w2
-9 + 6w + -1w2 = 2w + -2w + 2w2 + -2w2

Combine like terms: 2w + -2w = 0
-9 + 6w + -1w2 = 0 + 2w2 + -2w2
-9 + 6w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-9 + 6w + -1w2 = 0

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


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

Simplifying
-3 + w = 0

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

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

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

Simplifying
w = 3

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 = {3, 3}

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