(2w+7)w=99

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


Simplifying
(2w + 7) * w = 99

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

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

Solving
7w + 2w2 = 99

Solving for variable 'w'.

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

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

Factor a trinomial.
(-9 + -1w)(11 + -2w) = 0


Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve:

Simplifying
-9 + -1w = 0

Solving
-9 + -1w = 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 + -1w = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1w = 0 + 9
-1w = 0 + 9

Combine like terms: 0 + 9 = 9
-1w = 9

Divide each side by '-1'.
w = -9

Simplifying
w = -9

Subproblem 2
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
Solution
w = {-9, 5.5}

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