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

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

Simplifying
(2z + -1)(3z + -2) = 0

Reorder the terms:
(-1 + 2z)(3z + -2) = 0

Reorder the terms:
(-1 + 2z)(-2 + 3z) = 0

Multiply (-1 + 2z) * (-2 + 3z)
(-1(-2 + 3z) + 2z * (-2 + 3z)) = 0
((-2 * -1 + 3z * -1) + 2z * (-2 + 3z)) = 0
((2 + -3z) + 2z * (-2 + 3z)) = 0
(2 + -3z + (-2 * 2z + 3z * 2z)) = 0
(2 + -3z + (-4z + 6z2)) = 0

Combine like terms: -3z + -4z = -7z
(2 + -7z + 6z2) = 0

Solving
2 + -7z + 6z2 = 0

Solving for variable 'z'.

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

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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Subproblem 2
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
Solution
z = {0.5, 0.6666666667}