4x^2-x+1=x+3x^2

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

Simplifying
4x2 + -1x + 1 = x + 3x2

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

Solving
1 + -1x + 4x2 = x + 3x2

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(1 + -1x)(1 + -1x) = 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 + -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
Solution
x = {1, 1}