2x^2+14x+17=5

Solution for 2x^2+14x+17=5 equation:

Simplifying
2x2 + 14x + 17 = 5

Reorder the terms:
17 + 14x + 2x2 = 5

Solving
17 + 14x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
17 + -5 + 14x + 2x2 = 5 + -5

Combine like terms: 17 + -5 = 12
12 + 14x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
12 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 7x + x2) = 0

Factor a trinomial.
2((6 + x)(1 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
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 = {-6, -1}