4z(2z-3)=2z-3

Solution for 4z(2z-3)=2z-3 equation:

Simplifying
4z(2z + -3) = 2z + -3

Reorder the terms:
4z(-3 + 2z) = 2z + -3
(-3 * 4z + 2z * 4z) = 2z + -3
(-12z + 8z2) = 2z + -3

Reorder the terms:
-12z + 8z2 = -3 + 2z

Solving
-12z + 8z2 = -3 + 2z

Solving for variable 'z'.

Reorder the terms:
3 + -12z + -2z + 8z2 = -3 + 2z + 3 + -2z

Combine like terms: -12z + -2z = -14z
3 + -14z + 8z2 = -3 + 2z + 3 + -2z

Reorder the terms:
3 + -14z + 8z2 = -3 + 3 + 2z + -2z

Combine like terms: -3 + 3 = 0
3 + -14z + 8z2 = 0 + 2z + -2z
3 + -14z + 8z2 = 2z + -2z

Combine like terms: 2z + -2z = 0
3 + -14z + 8z2 = 0

Factor a trinomial.
(1 + -4z)(3 + -2z) = 0

Subproblem 1
Set the factor '(1 + -4z)' equal to zero and attempt to solve:

Simplifying
1 + -4z = 0

Solving
1 + -4z = 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 + -4z = 0 + -1

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

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

Divide each side by '-4'.
z = 0.25

Simplifying
z = 0.25
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 = {0.25, 1.5}