x(3x-4)=-1

Solution for x(3x-4)=-1 equation:

Simplifying
x(3x + -4) = -1

Reorder the terms:
x(-4 + 3x) = -1
(-4 * x + 3x * x) = -1
(-4x + 3x2) = -1

Solving
-4x + 3x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + -4x + 3x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -4x + 3x2 = 0

Factor a trinomial.
(1 + -3x)(1 + -1x) = 0

Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
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 = {0.3333333333, 1}