99=w(2w+7)

Solution for 99=w(2w+7) equation:

Simplifying
99 = w(2w + 7)

Reorder the terms:
99 = w(7 + 2w)
99 = (7 * w + 2w * w)
99 = (7w + 2w2)

Solving
99 = 7w + 2w2

Solving for variable 'w'.

Reorder the terms:
99 + -7w + -2w2 = 7w + -7w + 2w2 + -2w2

Combine like terms: 7w + -7w = 0
99 + -7w + -2w2 = 0 + 2w2 + -2w2
99 + -7w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
99 + -7w + -2w2 = 0

Factor a trinomial.
(11 + -2w)(9 + w) = 0

Subproblem 1
Set the factor '(11 + -2w)' equal to zero and attempt to solve:

Simplifying
11 + -2w = 0

Solving
11 + -2w = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2w = 0 + -11
-2w = 0 + -11

Combine like terms: 0 + -11 = -11
-2w = -11

Divide each side by '-2'.
w = 5.5

Simplifying
w = 5.5
Subproblem 2
Set the factor '(9 + w)' equal to zero and attempt to solve:

Simplifying
9 + w = 0

Solving
9 + w = 0

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

Add '-9' to each side of the equation.
9 + -9 + w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + w = 0 + -9
w = 0 + -9

Combine like terms: 0 + -9 = -9
w = -9

Simplifying
w = -9
Solution
w = {5.5, -9}