13x^2-27x+2=0

Solution for 13x^2-27x+2=0 equation:

Simplifying
13x2 + -27x + 2 = 0

Reorder the terms:
2 + -27x + 13x2 = 0

Solving
2 + -27x + 13x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -13x)(2 + -1x) = 0

Subproblem 1
Set the factor '(1 + -13x)' equal to zero and attempt to solve:

Simplifying
1 + -13x = 0

Solving
1 + -13x = 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 + -13x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -13x = 0 + -1
-13x = 0 + -1

Combine like terms: 0 + -1 = -1
-13x = -1

Divide each side by '-13'.
x = 0.07692307692

Simplifying
x = 0.07692307692
Subproblem 2
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
Solution
x = {0.07692307692, 2}