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

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

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

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

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

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

Combine like terms: -5x + -2x = -7x
0 = -2(10 + -7x + x2)
0 = (10 * -2 + -7x * -2 + x2 * -2)
0 = (-20 + 14x + -2x2)

Solving
0 = -20 + 14x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + -14x + 2x2 = -20 + 14x + -2x2 + 20 + -14x + 2x2

Reorder the terms:
20 + -14x + 2x2 = -20 + 20 + 14x + -14x + -2x2 + 2x2

Combine like terms: -20 + 20 = 0
20 + -14x + 2x2 = 0 + 14x + -14x + -2x2 + 2x2
20 + -14x + 2x2 = 14x + -14x + -2x2 + 2x2

Combine like terms: 14x + -14x = 0
20 + -14x + 2x2 = 0 + -2x2 + 2x2
20 + -14x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
20 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7x + x2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {2, 5}