w(w+17)=110

Solution for w(w+17)=110 equation:

Simplifying
w(w + 17) = 110

Reorder the terms:
w(17 + w) = 110
(17 * w + w * w) = 110
(17w + w2) = 110

Solving
17w + w2 = 110

Solving for variable 'w'.

Reorder the terms:
-110 + 17w + w2 = 110 + -110

Combine like terms: 110 + -110 = 0
-110 + 17w + w2 = 0

Factor a trinomial.
(-22 + -1w)(5 + -1w) = 0

Subproblem 1
Set the factor '(-22 + -1w)' equal to zero and attempt to solve:

Simplifying
-22 + -1w = 0

Solving
-22 + -1w = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1w = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1w = 0 + 22
-1w = 0 + 22

Combine like terms: 0 + 22 = 22
-1w = 22

Divide each side by '-1'.
w = -22

Simplifying
w = -22
Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

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

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

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-22, 5}