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

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

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

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

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

Multiply (-2 + 4X) * (3 + 6X)
(-2(3 + 6X) + 4X * (3 + 6X)) = 0
((3 * -2 + 6X * -2) + 4X * (3 + 6X)) = 0
((-6 + -12X) + 4X * (3 + 6X)) = 0
(-6 + -12X + (3 * 4X + 6X * 4X)) = 0
(-6 + -12X + (12X + 24X2)) = 0

Combine like terms: -12X + 12X = 0
(-6 + 0 + 24X2) = 0
(-6 + 24X2) = 0

Solving
-6 + 24X2 = 0

Solving for variable 'X'.

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

Add '6' to each side of the equation.
-6 + 6 + 24X2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 24X2 = 0 + 6
24X2 = 0 + 6

Combine like terms: 0 + 6 = 6
24X2 = 6

Divide each side by '24'.
X2 = 0.25

Simplifying
X2 = 0.25

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