2x^2-13x+31=x^2-2x+1

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Solution for 2x^2-13x+31=x^2-2x+1 equation: 


Simplifying
2x2 + -13x + 31 = x2 + -2x + 1

Reorder the terms:
31 + -13x + 2x2 = x2 + -2x + 1

Reorder the terms:
31 + -13x + 2x2 = 1 + -2x + x2

Solving
31 + -13x + 2x2 = 1 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
31 + -1 + -13x + 2x + 2x2 + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 31 + -1 = 30
30 + -13x + 2x + 2x2 + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: -13x + 2x = -11x
30 + -11x + 2x2 + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
30 + -11x + 1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Reorder the terms:
30 + -11x + 1x2 = 1 + -1 + -2x + 2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
30 + -11x + 1x2 = 0 + -2x + 2x + x2 + -1x2
30 + -11x + 1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
30 + -11x + 1x2 = 0 + x2 + -1x2
30 + -11x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + -11x + 1x2 = 0

Factor a trinomial.
(5 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {5, 6}

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