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

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

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

Reorder the terms:
7x(-5 + x) + (x + -5) = 0
(-5 * 7x + x * 7x) + (x + -5) = 0
(-35x + 7x2) + (x + -5) = 0

Reorder the terms:
-35x + 7x2 + (-5 + x) = 0

Remove parenthesis around (-5 + x)
-35x + 7x2 + -5 + x = 0

Reorder the terms:
-5 + -35x + x + 7x2 = 0

Combine like terms: -35x + x = -34x
-5 + -34x + 7x2 = 0

Solving
-5 + -34x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -7x)(5 + -1x) = 0

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

Simplifying
-1 + -7x = 0

Solving
-1 + -7x = 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 + -7x = 0 + 1

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

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

Divide each side by '-7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.1428571429, 5}