(2x-1)(6x+3)=0

Solution for (2x-1)(6x+3)=0 equation:

Simplifying
(2x + -1)(6x + 3) = 0

Reorder the terms:
(-1 + 2x)(6x + 3) = 0

Reorder the terms:
(-1 + 2x)(3 + 6x) = 0

Multiply (-1 + 2x) * (3 + 6x)
(-1(3 + 6x) + 2x * (3 + 6x)) = 0
((3 * -1 + 6x * -1) + 2x * (3 + 6x)) = 0
((-3 + -6x) + 2x * (3 + 6x)) = 0
(-3 + -6x + (3 * 2x + 6x * 2x)) = 0
(-3 + -6x + (6x + 12x2)) = 0

Combine like terms: -6x + 6x = 0
(-3 + 0 + 12x2) = 0
(-3 + 12x2) = 0

Solving
-3 + 12x2 = 0

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + 12x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 12x2 = 0 + 3
12x2 = 0 + 3

Combine like terms: 0 + 3 = 3
12x2 = 3

Divide each side by '12'.
x2 = 0.25

Simplifying
x2 = 0.25

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