3x^2-6x-2=-x^2+x

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Solution for 3x^2-6x-2=-x^2+x equation: 


Simplifying
3x2 + -6x + -2 = -1x2 + x

Reorder the terms:
-2 + -6x + 3x2 = -1x2 + x

Reorder the terms:
-2 + -6x + 3x2 = x + -1x2

Solving
-2 + -6x + 3x2 = x + -1x2

Solving for variable 'x'.

Reorder the terms:
-2 + -6x + -1x + 3x2 + x2 = x + -1x2 + -1x + x2

Combine like terms: -6x + -1x = -7x
-2 + -7x + 3x2 + x2 = x + -1x2 + -1x + x2

Combine like terms: 3x2 + x2 = 4x2
-2 + -7x + 4x2 = x + -1x2 + -1x + x2

Reorder the terms:
-2 + -7x + 4x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
-2 + -7x + 4x2 = 0 + -1x2 + x2
-2 + -7x + 4x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-2 + -7x + 4x2 = 0

Factor a trinomial.
(-1 + -4x)(2 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.25, 2}

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