22x+6=8x^2

Solution for 22x+6=8x^2 equation:

Simplifying
22x + 6 = 8x2

Reorder the terms:
6 + 22x = 8x2

Solving
6 + 22x = 8x2

Solving for variable 'x'.

Combine like terms: 8x2 + -8x2 = 0
6 + 22x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 11x + -4x2) = 0

Factor a trinomial.
2((3 + -1x)(1 + 4x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {3, -0.25}