(4z-2)(6z+3)=0

Solution for (4z-2)(6z+3)=0 equation:

Simplifying
(4z + -2)(6z + 3) = 0

Reorder the terms:
(-2 + 4z)(6z + 3) = 0

Reorder the terms:
(-2 + 4z)(3 + 6z) = 0

Multiply (-2 + 4z) * (3 + 6z)
(-2(3 + 6z) + 4z * (3 + 6z)) = 0
((3 * -2 + 6z * -2) + 4z * (3 + 6z)) = 0
((-6 + -12z) + 4z * (3 + 6z)) = 0
(-6 + -12z + (3 * 4z + 6z * 4z)) = 0
(-6 + -12z + (12z + 24z2)) = 0

Combine like terms: -12z + 12z = 0
(-6 + 0 + 24z2) = 0
(-6 + 24z2) = 0

Solving
-6 + 24z2 = 0

Solving for variable 'z'.

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

Add '6' to each side of the equation.
-6 + 6 + 24z2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 24z2 = 0 + 6
24z2 = 0 + 6

Combine like terms: 0 + 6 = 6
24z2 = 6

Divide each side by '24'.
z2 = 0.25

Simplifying
z2 = 0.25

Take the square root of each side:
z = {-0.5, 0.5}