3z^2-7z-6=0

Solution for 3z^2-7z-6=0 equation:

Simplifying
3z2 + -7z + -6 = 0

Reorder the terms:
-6 + -7z + 3z2 = 0

Solving
-6 + -7z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -3z)(3 + -1z) = 0

Subproblem 1
Set the factor '(-2 + -3z)' equal to zero and attempt to solve:

Simplifying
-2 + -3z = 0

Solving
-2 + -3z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3z = 0 + 2
-3z = 0 + 2

Combine like terms: 0 + 2 = 2
-3z = 2

Divide each side by '-3'.
z = -0.6666666667

Simplifying
z = -0.6666666667
Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

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

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

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

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {-0.6666666667, 3}