-2(x+3)(x-5)=0

Solution for -2(x+3)(x-5)=0 equation:

Simplifying
-2(x + 3)(x + -5) = 0

Reorder the terms:
-2(3 + x)(x + -5) = 0

Reorder the terms:
-2(3 + x)(-5 + x) = 0

Multiply (3 + x) * (-5 + x)
-2(3(-5 + x) + x(-5 + x)) = 0
-2((-5 * 3 + x * 3) + x(-5 + x)) = 0
-2((-15 + 3x) + x(-5 + x)) = 0
-2(-15 + 3x + (-5 * x + x * x)) = 0
-2(-15 + 3x + (-5x + x2)) = 0

Combine like terms: 3x + -5x = -2x
-2(-15 + -2x + x2) = 0
(-15 * -2 + -2x * -2 + x2 * -2) = 0
(30 + 4x + -2x2) = 0

Solving
30 + 4x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 2x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(3 + x)) = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {5, -3}