(4a+2)(2a-1)=0

Solution for (4a+2)(2a-1)=0 equation:

Simplifying
(4a + 2)(2a + -1) = 0

Reorder the terms:
(2 + 4a)(2a + -1) = 0

Reorder the terms:
(2 + 4a)(-1 + 2a) = 0

Multiply (2 + 4a) * (-1 + 2a)
(2(-1 + 2a) + 4a * (-1 + 2a)) = 0
((-1 * 2 + 2a * 2) + 4a * (-1 + 2a)) = 0
((-2 + 4a) + 4a * (-1 + 2a)) = 0
(-2 + 4a + (-1 * 4a + 2a * 4a)) = 0
(-2 + 4a + (-4a + 8a2)) = 0

Combine like terms: 4a + -4a = 0
(-2 + 0 + 8a2) = 0
(-2 + 8a2) = 0

Solving
-2 + 8a2 = 0

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + 8a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8a2 = 0 + 2
8a2 = 0 + 2

Combine like terms: 0 + 2 = 2
8a2 = 2

Divide each side by '8'.
a2 = 0.25

Simplifying
a2 = 0.25

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