1222=2x^2+24x+326

Solution for 1222=2x^2+24x+326 equation:

Simplifying
1222 = 2x2 + 24x + 326

Reorder the terms:
1222 = 326 + 24x + 2x2

Solving
1222 = 326 + 24x + 2x2

Solving for variable 'x'.

Combine like terms: 1222 + -326 = 896
896 + -24x + -2x2 = 326 + 24x + 2x2 + -326 + -24x + -2x2

Reorder the terms:
896 + -24x + -2x2 = 326 + -326 + 24x + -24x + 2x2 + -2x2

Combine like terms: 326 + -326 = 0
896 + -24x + -2x2 = 0 + 24x + -24x + 2x2 + -2x2
896 + -24x + -2x2 = 24x + -24x + 2x2 + -2x2

Combine like terms: 24x + -24x = 0
896 + -24x + -2x2 = 0 + 2x2 + -2x2
896 + -24x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
896 + -24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(448 + -12x + -1x2) = 0

Factor a trinomial.
2((16 + -1x)(28 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Subproblem 2
Set the factor '(28 + x)' equal to zero and attempt to solve:

Simplifying
28 + x = 0

Solving
28 + x = 0

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

Add '-28' to each side of the equation.
28 + -28 + x = 0 + -28

Combine like terms: 28 + -28 = 0
0 + x = 0 + -28
x = 0 + -28

Combine like terms: 0 + -28 = -28
x = -28

Simplifying
x = -28
Solution
x = {16, -28}