(2x-2)(x+5)=0

Solution for (2x-2)(x+5)=0 equation:

Simplifying
(2x + -2)(x + 5) = 0

Reorder the terms:
(-2 + 2x)(x + 5) = 0

Reorder the terms:
(-2 + 2x)(5 + x) = 0

Multiply (-2 + 2x) * (5 + x)
(-2(5 + x) + 2x * (5 + x)) = 0
((5 * -2 + x * -2) + 2x * (5 + x)) = 0
((-10 + -2x) + 2x * (5 + x)) = 0
(-10 + -2x + (5 * 2x + x * 2x)) = 0
(-10 + -2x + (10x + 2x2)) = 0

Combine like terms: -2x + 10x = 8x
(-10 + 8x + 2x2) = 0

Solving
-10 + 8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 4x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-5, 1}