20x^2=22x-6

Solution for 20x^2=22x-6 equation:

Simplifying
20x2 = 22x + -6

Reorder the terms:
20x2 = -6 + 22x

Solving
20x2 = -6 + 22x

Solving for variable 'x'.

Reorder the terms:
6 + -22x + 20x2 = -6 + 22x + 6 + -22x

Reorder the terms:
6 + -22x + 20x2 = -6 + 6 + 22x + -22x

Combine like terms: -6 + 6 = 0
6 + -22x + 20x2 = 0 + 22x + -22x
6 + -22x + 20x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
6 + -22x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -11x + 10x2) = 0

Factor a trinomial.
2((1 + -2x)(3 + -5x)) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0.5, 0.6}