6z^2-5z=6

Solution for 6z^2-5z=6 equation:

Simplifying
6z2 + -5z = 6

Reorder the terms:
-5z + 6z2 = 6

Solving
-5z + 6z2 = 6

Solving for variable 'z'.

Reorder the terms:
-6 + -5z + 6z2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -5z + 6z2 = 0

Factor a trinomial.
(-2 + -3z)(3 + -2z) = 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 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 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 + -2z = 0 + -3

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

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

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {-0.6666666667, 1.5}