0=w^2+14w+33

Solution for 0=w^2+14w+33 equation:

Simplifying
0 = w2 + 14w + 33

Reorder the terms:
0 = 33 + 14w + w2

Solving
0 = 33 + 14w + w2

Solving for variable 'w'.

Combine like terms: 0 + -33 = -33
-33 + -14w + -1w2 = 33 + 14w + w2 + -33 + -14w + -1w2

Reorder the terms:
-33 + -14w + -1w2 = 33 + -33 + 14w + -14w + w2 + -1w2

Combine like terms: 33 + -33 = 0
-33 + -14w + -1w2 = 0 + 14w + -14w + w2 + -1w2
-33 + -14w + -1w2 = 14w + -14w + w2 + -1w2

Combine like terms: 14w + -14w = 0
-33 + -14w + -1w2 = 0 + w2 + -1w2
-33 + -14w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-33 + -14w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(33 + 14w + w2) = 0

Factor a trinomial.
-1((11 + w)(3 + w)) = 0

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

Simplifying
11 + w = 0

Solving
11 + w = 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 + w = 0 + -11

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

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

Simplifying
w = -11
Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
Solution
w = {-11, -3}