(x-5)(7x+1)=-20(x-5)

Solution for (x-5)(7x+1)=-20(x-5) equation:

Simplifying
(x + -5)(7x + 1) = -20(x + -5)

Reorder the terms:
(-5 + x)(7x + 1) = -20(x + -5)

Reorder the terms:
(-5 + x)(1 + 7x) = -20(x + -5)

Multiply (-5 + x) * (1 + 7x)
(-5(1 + 7x) + x(1 + 7x)) = -20(x + -5)
((1 * -5 + 7x * -5) + x(1 + 7x)) = -20(x + -5)
((-5 + -35x) + x(1 + 7x)) = -20(x + -5)
(-5 + -35x + (1 * x + 7x * x)) = -20(x + -5)
(-5 + -35x + (1x + 7x2)) = -20(x + -5)

Combine like terms: -35x + 1x = -34x
(-5 + -34x + 7x2) = -20(x + -5)

Reorder the terms:
-5 + -34x + 7x2 = -20(-5 + x)
-5 + -34x + 7x2 = (-5 * -20 + x * -20)
-5 + -34x + 7x2 = (100 + -20x)

Solving
-5 + -34x + 7x2 = 100 + -20x

Solving for variable 'x'.

Reorder the terms:
-5 + -100 + -34x + 20x + 7x2 = 100 + -20x + -100 + 20x

Combine like terms: -5 + -100 = -105
-105 + -34x + 20x + 7x2 = 100 + -20x + -100 + 20x

Combine like terms: -34x + 20x = -14x
-105 + -14x + 7x2 = 100 + -20x + -100 + 20x

Reorder the terms:
-105 + -14x + 7x2 = 100 + -100 + -20x + 20x

Combine like terms: 100 + -100 = 0
-105 + -14x + 7x2 = 0 + -20x + 20x
-105 + -14x + 7x2 = -20x + 20x

Combine like terms: -20x + 20x = 0
-105 + -14x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-15 + -2x + x2) = 0

Factor a trinomial.
7((-3 + -1x)(5 + -1x)) = 0

Ignore the factor 7.
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 '(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 = {-3, 5}