x(4x+22)=12

Solution for x(4x+22)=12 equation:

Simplifying
x(4x + 22) = 12

Reorder the terms:
x(22 + 4x) = 12
(22 * x + 4x * x) = 12
(22x + 4x2) = 12

Solving
22x + 4x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 22x + 4x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 22x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 11x + 2x2) = 0

Factor a trinomial.
2((-6 + -1x)(1 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
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
Solution
x = {-6, 0.5}