2w^2+4w+2=8

Solution for 2w^2+4w+2=8 equation:

Simplifying
2w2 + 4w + 2 = 8

Reorder the terms:
2 + 4w + 2w2 = 8

Solving
2 + 4w + 2w2 = 8

Solving for variable 'w'.

Reorder the terms:
2 + -8 + 4w + 2w2 = 8 + -8

Combine like terms: 2 + -8 = -6
-6 + 4w + 2w2 = 8 + -8

Combine like terms: 8 + -8 = 0
-6 + 4w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2w + w2) = 0

Factor a trinomial.
2((-3 + -1w)(1 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
w = {-3, 1}