4x^2+34x+66=0

Solution for 4x^2+34x+66=0 equation:

Simplifying
4x2 + 34x + 66 = 0

Reorder the terms:
66 + 34x + 4x2 = 0

Solving
66 + 34x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(33 + 17x + 2x2) = 0

Factor a trinomial.
2((11 + 2x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + 2x)' equal to zero and attempt to solve:

Simplifying
11 + 2x = 0

Solving
11 + 2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2x = 0 + -11
2x = 0 + -11

Combine like terms: 0 + -11 = -11
2x = -11

Divide each side by '2'.
x = -5.5

Simplifying
x = -5.5
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {-5.5, -3}