(x-7)(2x-6)=0

Solution for (x-7)(2x-6)=0 equation:

Simplifying
(x + -7)(2x + -6) = 0

Reorder the terms:
(-7 + x)(2x + -6) = 0

Reorder the terms:
(-7 + x)(-6 + 2x) = 0

Multiply (-7 + x) * (-6 + 2x)
(-7(-6 + 2x) + x(-6 + 2x)) = 0
((-6 * -7 + 2x * -7) + x(-6 + 2x)) = 0
((42 + -14x) + x(-6 + 2x)) = 0
(42 + -14x + (-6 * x + 2x * x)) = 0
(42 + -14x + (-6x + 2x2)) = 0

Combine like terms: -14x + -6x = -20x
(42 + -20x + 2x2) = 0

Solving
42 + -20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -10x + x2) = 0

Factor a trinomial.
2((3 + -1x)(7 + -1x)) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {3, 7}