x(21x+1)=2

Solution for x(21x+1)=2 equation:

Simplifying
x(21x + 1) = 2

Reorder the terms:
x(1 + 21x) = 2
(1 * x + 21x * x) = 2
(1x + 21x2) = 2

Solving
1x + 21x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 1x + 21x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 1x + 21x2 = 0

Factor a trinomial.
(-1 + -3x)(2 + -7x) = 0

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

Simplifying
-1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 2
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {-0.3333333333, 0.2857142857}