(6-x)(8x+2)=0

Solution for (6-x)(8x+2)=0 equation:

Simplifying
(6 + -1x)(8x + 2) = 0

Reorder the terms:
(6 + -1x)(2 + 8x) = 0

Multiply (6 + -1x) * (2 + 8x)
(6(2 + 8x) + -1x * (2 + 8x)) = 0
((2 * 6 + 8x * 6) + -1x * (2 + 8x)) = 0
((12 + 48x) + -1x * (2 + 8x)) = 0
(12 + 48x + (2 * -1x + 8x * -1x)) = 0
(12 + 48x + (-2x + -8x2)) = 0

Combine like terms: 48x + -2x = 46x
(12 + 46x + -8x2) = 0

Solving
12 + 46x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 23x + -4x2) = 0

Factor a trinomial.
2((6 + -1x)(1 + 4x)) = 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 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {6, -0.25}