3z^2-4z=-1

Solution for 3z^2-4z=-1 equation:

Simplifying
3z2 + -4z = -1

Reorder the terms:
-4z + 3z2 = -1

Solving
-4z + 3z2 = -1

Solving for variable 'z'.

Reorder the terms:
1 + -4z + 3z2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -4z + 3z2 = 0

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

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

Simplifying
1 + -3z = 0

Solving
1 + -3z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -3z = 0 + -1

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

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

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

Simplifying
z = 0.3333333333
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1z = 0 + -1
-1z = 0 + -1

Combine like terms: 0 + -1 = -1
-1z = -1

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {0.3333333333, 1}