w^2+6w+9=361

Solution for w^2+6w+9=361 equation:

Simplifying
w2 + 6w + 9 = 361

Reorder the terms:
9 + 6w + w2 = 361

Solving
9 + 6w + w2 = 361

Solving for variable 'w'.

Reorder the terms:
9 + -361 + 6w + w2 = 361 + -361

Combine like terms: 9 + -361 = -352
-352 + 6w + w2 = 361 + -361

Combine like terms: 361 + -361 = 0
-352 + 6w + w2 = 0

Factor a trinomial.
(-22 + -1w)(16 + -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 '(16 + -1w)' equal to zero and attempt to solve:

Simplifying
16 + -1w = 0

Solving
16 + -1w = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1w = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1w = 0 + -16
-1w = 0 + -16

Combine like terms: 0 + -16 = -16
-1w = -16

Divide each side by '-1'.
w = 16

Simplifying
w = 16
Solution
w = {-22, 16}