123x^2-492x+813=444

Solution for 123x^2-492x+813=444 equation:

Simplifying
123x2 + -492x + 813 = 444

Reorder the terms:
813 + -492x + 123x2 = 444

Solving
813 + -492x + 123x2 = 444

Solving for variable 'x'.

Reorder the terms:
813 + -444 + -492x + 123x2 = 444 + -444

Combine like terms: 813 + -444 = 369
369 + -492x + 123x2 = 444 + -444

Combine like terms: 444 + -444 = 0
369 + -492x + 123x2 = 0

Factor out the Greatest Common Factor (GCF), '123'.
123(3 + -4x + x2) = 0

Factor a trinomial.
123((1 + -1x)(3 + -1x)) = 0

Ignore the factor 123.
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}