6x^2-2x+1=4x^2+x

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Solution for 6x^2-2x+1=4x^2+x equation: 


Simplifying
6x2 + -2x + 1 = 4x2 + x

Reorder the terms:
1 + -2x + 6x2 = 4x2 + x

Reorder the terms:
1 + -2x + 6x2 = x + 4x2

Solving
1 + -2x + 6x2 = x + 4x2

Solving for variable 'x'.

Reorder the terms:
1 + -2x + -1x + 6x2 + -4x2 = x + 4x2 + -1x + -4x2

Combine like terms: -2x + -1x = -3x
1 + -3x + 6x2 + -4x2 = x + 4x2 + -1x + -4x2

Combine like terms: 6x2 + -4x2 = 2x2
1 + -3x + 2x2 = x + 4x2 + -1x + -4x2

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

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

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

Factor a trinomial.
(1 + -2x)(1 + -1x) = 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 + -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 = {0.5, 1}

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