(w+2)(w+2)=2w^2+5w+2

Solution for (w+2)(w+2)=2w^2+5w+2 equation:

Simplifying
(w + 2)(w + 2) = 2w2 + 5w + 2

Reorder the terms:
(2 + w)(w + 2) = 2w2 + 5w + 2

Reorder the terms:
(2 + w)(2 + w) = 2w2 + 5w + 2

Multiply (2 + w) * (2 + w)
(2(2 + w) + w(2 + w)) = 2w2 + 5w + 2
((2 * 2 + w * 2) + w(2 + w)) = 2w2 + 5w + 2
((4 + 2w) + w(2 + w)) = 2w2 + 5w + 2
(4 + 2w + (2 * w + w * w)) = 2w2 + 5w + 2
(4 + 2w + (2w + w2)) = 2w2 + 5w + 2

Combine like terms: 2w + 2w = 4w
(4 + 4w + w2) = 2w2 + 5w + 2

Reorder the terms:
4 + 4w + w2 = 2 + 5w + 2w2

Solving
4 + 4w + w2 = 2 + 5w + 2w2

Solving for variable 'w'.

Reorder the terms:
4 + -2 + 4w + -5w + w2 + -2w2 = 2 + 5w + 2w2 + -2 + -5w + -2w2

Combine like terms: 4 + -2 = 2
2 + 4w + -5w + w2 + -2w2 = 2 + 5w + 2w2 + -2 + -5w + -2w2

Combine like terms: 4w + -5w = -1w
2 + -1w + w2 + -2w2 = 2 + 5w + 2w2 + -2 + -5w + -2w2

Combine like terms: w2 + -2w2 = -1w2
2 + -1w + -1w2 = 2 + 5w + 2w2 + -2 + -5w + -2w2

Reorder the terms:
2 + -1w + -1w2 = 2 + -2 + 5w + -5w + 2w2 + -2w2

Combine like terms: 2 + -2 = 0
2 + -1w + -1w2 = 0 + 5w + -5w + 2w2 + -2w2
2 + -1w + -1w2 = 5w + -5w + 2w2 + -2w2

Combine like terms: 5w + -5w = 0
2 + -1w + -1w2 = 0 + 2w2 + -2w2
2 + -1w + -1w2 = 2w2 + -2w2

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

Factor a trinomial.
(1 + -1w)(2 + w) = 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 '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

Simplifying
w = -2
Solution
w = {1, -2}