(10-2x)(6-2x)=12

Solution for (10-2x)(6-2x)=12 equation:

Simplifying
(10 + -2x)(6 + -2x) = 12

Multiply (10 + -2x) * (6 + -2x)
(10(6 + -2x) + -2x * (6 + -2x)) = 12
((6 * 10 + -2x * 10) + -2x * (6 + -2x)) = 12
((60 + -20x) + -2x * (6 + -2x)) = 12
(60 + -20x + (6 * -2x + -2x * -2x)) = 12
(60 + -20x + (-12x + 4x2)) = 12

Combine like terms: -20x + -12x = -32x
(60 + -32x + 4x2) = 12

Solving
60 + -32x + 4x2 = 12

Solving for variable 'x'.

Reorder the terms:
60 + -12 + -32x + 4x2 = 12 + -12

Combine like terms: 60 + -12 = 48
48 + -32x + 4x2 = 12 + -12

Combine like terms: 12 + -12 = 0
48 + -32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + -8x + x2) = 0

Factor a trinomial.
4((2 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
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
Solution
x = {2, 6}