4x^2+3x+1=2

Solution for 4x^2+3x+1=2 equation:

Simplifying
4x2 + 3x + 1 = 2

Reorder the terms:
1 + 3x + 4x2 = 2

Solving
1 + 3x + 4x2 = 2

Solving for variable 'x'.

Reorder the terms:
1 + -2 + 3x + 4x2 = 2 + -2

Combine like terms: 1 + -2 = -1
-1 + 3x + 4x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-1 + 3x + 4x2 = 0

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

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
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 = {-1, 0.25}