4z^2=6z

Solution for 4z^2=6z equation:

Simplifying
4z2 = 6z

Solving
4z2 = 6z

Solving for variable 'z'.

Reorder the terms:
-6z + 4z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
-6z + 4z2 = 0

Factor out the Greatest Common Factor (GCF), '2z'.
2z(-3 + 2z) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
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, 1.5}