x^2+34x+33=0

Solution for x^2+34x+33=0 equation:

Simplifying
x2 + 34x + 33 = 0

Reorder the terms:
33 + 34x + x2 = 0

Solving
33 + 34x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(33 + x)(1 + x) = 0

Subproblem 1
Set the factor '(33 + x)' equal to zero and attempt to solve:

Simplifying
33 + x = 0

Solving
33 + x = 0

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

Add '-33' to each side of the equation.
33 + -33 + x = 0 + -33

Combine like terms: 33 + -33 = 0
0 + x = 0 + -33
x = 0 + -33

Combine like terms: 0 + -33 = -33
x = -33

Simplifying
x = -33
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-33, -1}