2x^2=20x+22

Solution for 2x^2=20x+22 equation:

Simplifying
2x2 = 20x + 22

Reorder the terms:
2x2 = 22 + 20x

Solving
2x2 = 22 + 20x

Solving for variable 'x'.

Reorder the terms:
-22 + -20x + 2x2 = 22 + 20x + -22 + -20x

Reorder the terms:
-22 + -20x + 2x2 = 22 + -22 + 20x + -20x

Combine like terms: 22 + -22 = 0
-22 + -20x + 2x2 = 0 + 20x + -20x
-22 + -20x + 2x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
-22 + -20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -10x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(11 + -1x)) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 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 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-1, 11}