2z(3z-1)=9z-3

Solution for 2z(3z-1)=9z-3 equation:

Simplifying
2z(3z + -1) = 9z + -3

Reorder the terms:
2z(-1 + 3z) = 9z + -3
(-1 * 2z + 3z * 2z) = 9z + -3
(-2z + 6z2) = 9z + -3

Reorder the terms:
-2z + 6z2 = -3 + 9z

Solving
-2z + 6z2 = -3 + 9z

Solving for variable 'z'.

Reorder the terms:
3 + -2z + -9z + 6z2 = -3 + 9z + 3 + -9z

Combine like terms: -2z + -9z = -11z
3 + -11z + 6z2 = -3 + 9z + 3 + -9z

Reorder the terms:
3 + -11z + 6z2 = -3 + 3 + 9z + -9z

Combine like terms: -3 + 3 = 0
3 + -11z + 6z2 = 0 + 9z + -9z
3 + -11z + 6z2 = 9z + -9z

Combine like terms: 9z + -9z = 0
3 + -11z + 6z2 = 0

Factor a trinomial.
(1 + -3z)(3 + -2z) = 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 '(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 = {0.3333333333, 1.5}