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

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

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

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

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

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

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

Solving
30 + -13x + x2 = -10

Solving for variable 'x'.

Reorder the terms:
30 + 10 + -13x + x2 = -10 + 10

Combine like terms: 30 + 10 = 40
40 + -13x + x2 = -10 + 10

Combine like terms: -10 + 10 = 0
40 + -13x + x2 = 0

Factor a trinomial.
(5 + -1x)(8 + -1x) = 0

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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {5, 8}