4x(3x+1)=1

Solution for 4x(3x+1)=1 equation:

Simplifying
4x(3x + 1) = 1

Reorder the terms:
4x(1 + 3x) = 1
(1 * 4x + 3x * 4x) = 1
(4x + 12x2) = 1

Solving
4x + 12x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 4x + 12x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 4x + 12x2 = 0

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

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 '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

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

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

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {-0.5, 0.1666666667}