(7x-7)(x-3)=0

Solution for (7x-7)(x-3)=0 equation:

Simplifying
(7x + -7)(x + -3) = 0

Reorder the terms:
(-7 + 7x)(x + -3) = 0

Reorder the terms:
(-7 + 7x)(-3 + x) = 0

Multiply (-7 + 7x) * (-3 + x)
(-7(-3 + x) + 7x * (-3 + x)) = 0
((-3 * -7 + x * -7) + 7x * (-3 + x)) = 0
((21 + -7x) + 7x * (-3 + x)) = 0
(21 + -7x + (-3 * 7x + x * 7x)) = 0
(21 + -7x + (-21x + 7x2)) = 0

Combine like terms: -7x + -21x = -28x
(21 + -28x + 7x2) = 0

Solving
21 + -28x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + -4x + x2) = 0

Factor a trinomial.
7((1 + -1x)(3 + -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 '(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
Solution
x = {1, 3}