(x-7)(3x-5)-(x-7)=0

Solution for (x-7)(3x-5)-(x-7)=0 equation:

Simplifying
(x + -7)(3x + -5) + -1(x + -7) = 0

Reorder the terms:
(-7 + x)(3x + -5) + -1(x + -7) = 0

Reorder the terms:
(-7 + x)(-5 + 3x) + -1(x + -7) = 0

Multiply (-7 + x) * (-5 + 3x)
(-7(-5 + 3x) + x(-5 + 3x)) + -1(x + -7) = 0
((-5 * -7 + 3x * -7) + x(-5 + 3x)) + -1(x + -7) = 0
((35 + -21x) + x(-5 + 3x)) + -1(x + -7) = 0
(35 + -21x + (-5 * x + 3x * x)) + -1(x + -7) = 0
(35 + -21x + (-5x + 3x2)) + -1(x + -7) = 0

Combine like terms: -21x + -5x = -26x
(35 + -26x + 3x2) + -1(x + -7) = 0

Reorder the terms:
35 + -26x + 3x2 + -1(-7 + x) = 0
35 + -26x + 3x2 + (-7 * -1 + x * -1) = 0
35 + -26x + 3x2 + (7 + -1x) = 0

Reorder the terms:
35 + 7 + -26x + -1x + 3x2 = 0

Combine like terms: 35 + 7 = 42
42 + -26x + -1x + 3x2 = 0

Combine like terms: -26x + -1x = -27x
42 + -27x + 3x2 = 0

Solving
42 + -27x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -9x + x2) = 0

Factor a trinomial.
3((2 + -1x)(7 + -1x)) = 0

Ignore the factor 3.
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 '(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 = {2, 7}