(x-5)(x+1)=2(2-2)

Solution for (x-5)(x+1)=2(2-2) equation:

Simplifying
(x + -5)(x + 1) = 2(2 + -2)

Reorder the terms:
(-5 + x)(x + 1) = 2(2 + -2)

Reorder the terms:
(-5 + x)(1 + x) = 2(2 + -2)

Multiply (-5 + x) * (1 + x)
(-5(1 + x) + x(1 + x)) = 2(2 + -2)
((1 * -5 + x * -5) + x(1 + x)) = 2(2 + -2)
((-5 + -5x) + x(1 + x)) = 2(2 + -2)
(-5 + -5x + (1 * x + x * x)) = 2(2 + -2)
(-5 + -5x + (1x + x2)) = 2(2 + -2)

Combine like terms: -5x + 1x = -4x
(-5 + -4x + x2) = 2(2 + -2)

Combine like terms: 2 + -2 = 0
-5 + -4x + x2 = 2(0)

Multiply 2 * 0
-5 + -4x + x2 = 0

Anything times zero is zero.
-5 + -4x + x2 = 0

Solving
-5 + -4x + x2 = 0

Solving for variable 'x'.

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

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 '(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 = {-1, 5}