12x^2=13x-1

Solution for 12x^2=13x-1 equation:

Simplifying
12x2 = 13x + -1

Reorder the terms:
12x2 = -1 + 13x

Solving
12x2 = -1 + 13x

Solving for variable 'x'.

Reorder the terms:
1 + -13x + 12x2 = -1 + 13x + 1 + -13x

Reorder the terms:
1 + -13x + 12x2 = -1 + 1 + 13x + -13x

Combine like terms: -1 + 1 = 0
1 + -13x + 12x2 = 0 + 13x + -13x
1 + -13x + 12x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
1 + -13x + 12x2 = 0

Factor a trinomial.
(1 + -12x)(1 + -1x) = 0

Subproblem 1
Set the factor '(1 + -12x)' equal to zero and attempt to solve:

Simplifying
1 + -12x = 0

Solving
1 + -12x = 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 + -12x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -12x = 0 + -1
-12x = 0 + -1

Combine like terms: 0 + -1 = -1
-12x = -1

Divide each side by '-12'.
x = 0.08333333333

Simplifying
x = 0.08333333333
Subproblem 2
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
Solution
x = {0.08333333333, 1}