2x^2+22x+43=-5

Solution for 2x^2+22x+43=-5 equation:

Simplifying
2x2 + 22x + 43 = -5

Reorder the terms:
43 + 22x + 2x2 = -5

Solving
43 + 22x + 2x2 = -5

Solving for variable 'x'.

Reorder the terms:
43 + 5 + 22x + 2x2 = -5 + 5

Combine like terms: 43 + 5 = 48
48 + 22x + 2x2 = -5 + 5

Combine like terms: -5 + 5 = 0
48 + 22x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 11x + x2) = 0

Factor a trinomial.
2((8 + x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
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 = {-8, -3}