(4x-2)(x+6)=0

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

Simplifying
(4x + -2)(x + 6) = 0

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

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

Multiply (-2 + 4x) * (6 + x)
(-2(6 + x) + 4x * (6 + x)) = 0
((6 * -2 + x * -2) + 4x * (6 + x)) = 0
((-12 + -2x) + 4x * (6 + x)) = 0
(-12 + -2x + (6 * 4x + x * 4x)) = 0
(-12 + -2x + (24x + 4x2)) = 0

Combine like terms: -2x + 24x = 22x
(-12 + 22x + 4x2) = 0

Solving
-12 + 22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 11x + 2x2) = 0

Factor a trinomial.
2((-6 + -1x)(1 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 0.5}