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

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

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

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

Multiply (1 + 2x) * (6 + -2x)
(1(6 + -2x) + 2x * (6 + -2x)) = 0
((6 * 1 + -2x * 1) + 2x * (6 + -2x)) = 0
((6 + -2x) + 2x * (6 + -2x)) = 0
(6 + -2x + (6 * 2x + -2x * 2x)) = 0
(6 + -2x + (12x + -4x2)) = 0

Combine like terms: -2x + 12x = 10x
(6 + 10x + -4x2) = 0

Solving
6 + 10x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5x + -2x2) = 0

Factor a trinomial.
2((3 + -1x)(1 + 2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {3, -0.5}