(X-3)*(2X-10)=0

Solution for (X-3)*(2X-10)=0 equation:

Simplifying
(X + -3)(2X + -10) = 0

Reorder the terms:
(-3 + X)(2X + -10) = 0

Reorder the terms:
(-3 + X)(-10 + 2X) = 0

Multiply (-3 + X) * (-10 + 2X)
(-3(-10 + 2X) + X(-10 + 2X)) = 0
((-10 * -3 + 2X * -3) + X(-10 + 2X)) = 0
((30 + -6X) + X(-10 + 2X)) = 0
(30 + -6X + (-10 * X + 2X * X)) = 0
(30 + -6X + (-10X + 2X2)) = 0

Combine like terms: -6X + -10X = -16X
(30 + -16X + 2X2) = 0

Solving
30 + -16X + 2X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -8X + X2) = 0

Factor a trinomial.
2((3 + -1X)(5 + -1X)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {3, 5}