27x^2-53x-2=0

Solution for 27x^2-53x-2=0 equation:

Simplifying
27x2 + -53x + -2 = 0

Reorder the terms:
-2 + -53x + 27x2 = 0

Solving
-2 + -53x + 27x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -27x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -27x)' equal to zero and attempt to solve:

Simplifying
-1 + -27x = 0

Solving
-1 + -27x = 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 + -27x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -27x = 0 + 1
-27x = 0 + 1

Combine like terms: 0 + 1 = 1
-27x = 1

Divide each side by '-27'.
x = -0.03703703704

Simplifying
x = -0.03703703704
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 = {-0.03703703704, 2}