(x-12)(7x-7)=0

Solution for (x-12)(7x-7)=0 equation:

Simplifying
(x + -12)(7x + -7) = 0

Reorder the terms:
(-12 + x)(7x + -7) = 0

Reorder the terms:
(-12 + x)(-7 + 7x) = 0

Multiply (-12 + x) * (-7 + 7x)
(-12(-7 + 7x) + x(-7 + 7x)) = 0
((-7 * -12 + 7x * -12) + x(-7 + 7x)) = 0
((84 + -84x) + x(-7 + 7x)) = 0
(84 + -84x + (-7 * x + 7x * x)) = 0
(84 + -84x + (-7x + 7x2)) = 0

Combine like terms: -84x + -7x = -91x
(84 + -91x + 7x2) = 0

Solving
84 + -91x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(12 + -13x + x2) = 0

Factor a trinomial.
7((1 + -1x)(12 + -1x)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {1, 12}