84=w(2+2w)

Solution for 84=w(2+2w) equation:

Simplifying
84 = w(2 + 2w)
84 = (2 * w + 2w * w)
84 = (2w + 2w2)

Solving
84 = 2w + 2w2

Solving for variable 'w'.

Reorder the terms:
84 + -2w + -2w2 = 2w + -2w + 2w2 + -2w2

Combine like terms: 2w + -2w = 0
84 + -2w + -2w2 = 0 + 2w2 + -2w2
84 + -2w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
84 + -2w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + -1w + -1w2) = 0

Factor a trinomial.
2((6 + -1w)(7 + w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Subproblem 2
Set the factor '(7 + w)' equal to zero and attempt to solve:

Simplifying
7 + w = 0

Solving
7 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + w = 0 + -7
w = 0 + -7

Combine like terms: 0 + -7 = -7
w = -7

Simplifying
w = -7
Solution
w = {6, -7}