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

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

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

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

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

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

Combine like terms: -1x + 7x = 6x
(-7 + 6x + x2) = 20

Solving
-7 + 6x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-7 + -20 + 6x + x2 = 20 + -20

Combine like terms: -7 + -20 = -27
-27 + 6x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-27 + 6x + x2 = 0

Factor a trinomial.
(-9 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
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 = {-9, 3}