x(6x-7)=-1

Solution for x(6x-7)=-1 equation:

Simplifying
x(6x + -7) = -1

Reorder the terms:
x(-7 + 6x) = -1
(-7 * x + 6x * x) = -1
(-7x + 6x2) = -1

Solving
-7x + 6x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + -7x + 6x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -7x + 6x2 = 0

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

Subproblem 1
Set the factor '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x = 0 + -1
-6x = 0 + -1

Combine like terms: 0 + -1 = -1
-6x = -1

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
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 = {0.1666666667, 1}