(x-10)(x-3)=0

Solution for (x-10)(x-3)=0 equation:

Simplifying
(x + -10)(x + -3) = 0

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

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

Multiply (-10 + x) * (-3 + x)
(-10(-3 + x) + x(-3 + x)) = 0
((-3 * -10 + x * -10) + x(-3 + x)) = 0
((30 + -10x) + x(-3 + x)) = 0
(30 + -10x + (-3 * x + x * x)) = 0
(30 + -10x + (-3x + x2)) = 0

Combine like terms: -10x + -3x = -13x
(30 + -13x + x2) = 0

Solving
30 + -13x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(10 + -1x) = 0

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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {3, 10}