X-2=3X^2-5X+1

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Solution for X-2=3X^2-5X+1 equation: 


Simplifying
X + -2 = 3X2 + -5X + 1

Reorder the terms:
-2 + X = 3X2 + -5X + 1

Reorder the terms:
-2 + X = 1 + -5X + 3X2

Solving
-2 + X = 1 + -5X + 3X2

Solving for variable 'X'.

Reorder the terms:
-2 + -1 + X + 5X + -3X2 = 1 + -5X + 3X2 + -1 + 5X + -3X2

Combine like terms: -2 + -1 = -3
-3 + X + 5X + -3X2 = 1 + -5X + 3X2 + -1 + 5X + -3X2

Combine like terms: X + 5X = 6X
-3 + 6X + -3X2 = 1 + -5X + 3X2 + -1 + 5X + -3X2

Reorder the terms:
-3 + 6X + -3X2 = 1 + -1 + -5X + 5X + 3X2 + -3X2

Combine like terms: 1 + -1 = 0
-3 + 6X + -3X2 = 0 + -5X + 5X + 3X2 + -3X2
-3 + 6X + -3X2 = -5X + 5X + 3X2 + -3X2

Combine like terms: -5X + 5X = 0
-3 + 6X + -3X2 = 0 + 3X2 + -3X2
-3 + 6X + -3X2 = 3X2 + -3X2

Combine like terms: 3X2 + -3X2 = 0
-3 + 6X + -3X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2X + -1X2) = 0

Factor a trinomial.
3((-1 + X)(1 + -1X)) = 0

Ignore the factor 3.

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

Simplifying
-1 + X = 0

Solving
-1 + X = 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 + X = 0 + 1

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

Combine like terms: 0 + 1 = 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}

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