21x^2+x+1=3

Solution for 21x^2+x+1=3 equation:

Simplifying
21x2 + x + 1 = 3

Reorder the terms:
1 + x + 21x2 = 3

Solving
1 + x + 21x2 = 3

Solving for variable 'x'.

Reorder the terms:
1 + -3 + x + 21x2 = 3 + -3

Combine like terms: 1 + -3 = -2
-2 + x + 21x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-2 + x + 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}