3x^2-21x+31=1

Solution for 3x^2-21x+31=1 equation:

Simplifying
3x2 + -21x + 31 = 1

Reorder the terms:
31 + -21x + 3x2 = 1

Solving
31 + -21x + 3x2 = 1

Solving for variable 'x'.

Reorder the terms:
31 + -1 + -21x + 3x2 = 1 + -1

Combine like terms: 31 + -1 = 30
30 + -21x + 3x2 = 1 + -1

Combine like terms: 1 + -1 = 0
30 + -21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -7x + x2) = 0

Factor a trinomial.
3((2 + -1x)(5 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
x = {2, 5}