2w(w+1)=w^2+8

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Solution for 2w(w+1)=w^2+8 equation: 


Simplifying
2w(w + 1) = w2 + 8

Reorder the terms:
2w(1 + w) = w2 + 8
(1 * 2w + w * 2w) = w2 + 8
(2w + 2w2) = w2 + 8

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

Solving
2w + 2w2 = 8 + w2

Solving for variable 'w'.

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

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

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

Combine like terms: 8 + -8 = 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.
(-4 + -1w)(2 + -1w) = 0


Subproblem 1
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

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 = {-4, 2}

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