3x^2-15x+19=1

Solution for 3x^2-15x+19=1 equation:

Simplifying
3x2 + -15x + 19 = 1

Reorder the terms:
19 + -15x + 3x2 = 1

Solving
19 + -15x + 3x2 = 1

Solving for variable 'x'.

Reorder the terms:
19 + -1 + -15x + 3x2 = 1 + -1

Combine like terms: 19 + -1 = 18
18 + -15x + 3x2 = 1 + -1

Combine like terms: 1 + -1 = 0
18 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -5x + x2) = 0

Factor a trinomial.
3((2 + -1x)(3 + -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 '(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 = {2, 3}