6X^2-13X=19

Solution for 6X^2-13X=19 equation:

Simplifying
6X2 + -13X = 19

Reorder the terms:
-13X + 6X2 = 19

Solving
-13X + 6X2 = 19

Solving for variable 'X'.

Reorder the terms:
-19 + -13X + 6X2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + -13X + 6X2 = 0

Factor a trinomial.
(-1 + -1X)(19 + -6X) = 0

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 '(19 + -6X)' equal to zero and attempt to solve:

Simplifying
19 + -6X = 0

Solving
19 + -6X = 0

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

Add '-19' to each side of the equation.
19 + -19 + -6X = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -6X = 0 + -19
-6X = 0 + -19

Combine like terms: 0 + -19 = -19
-6X = -19

Divide each side by '-6'.
X = 3.166666667

Simplifying
X = 3.166666667
Solution
X = {-1, 3.166666667}