w^2+17w=38

Solution for w^2+17w=38 equation:

Simplifying
w2 + 17w = 38

Reorder the terms:
17w + w2 = 38

Solving
17w + w2 = 38

Solving for variable 'w'.

Reorder the terms:
-38 + 17w + w2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + 17w + w2 = 0

Factor a trinomial.
(-19 + -1w)(2 + -1w) = 0

Subproblem 1
Set the factor '(-19 + -1w)' equal to zero and attempt to solve:

Simplifying
-19 + -1w = 0

Solving
-19 + -1w = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1w = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1w = 0 + 19
-1w = 0 + 19

Combine like terms: 0 + 19 = 19
-1w = 19

Divide each side by '-1'.
w = -19

Simplifying
w = -19
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-19, 2}