3x^2-12x+31=22

Solution for 3x^2-12x+31=22 equation:

Simplifying
3x2 + -12x + 31 = 22

Reorder the terms:
31 + -12x + 3x2 = 22

Solving
31 + -12x + 3x2 = 22

Solving for variable 'x'.

Reorder the terms:
31 + -22 + -12x + 3x2 = 22 + -22

Combine like terms: 31 + -22 = 9
9 + -12x + 3x2 = 22 + -22

Combine like terms: 22 + -22 = 0
9 + -12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -4x + x2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}